Forgive me that I reply only so late, but I had to get some information on the subject to be able to reply something substantial (sadly, my knowledge about this early period is quite limited). As I said above, I mostly read germanophone authors (Bleicken, Rainer, Bringmann...) who are quite critical of Roman and Greek historiography. The first Roman historian Fabius Pictor lived at the end of the 3rd century BCE, and only the events after 367 BCE are considered as confirmed. The preceeding centuries have been filigreed by Greeks and Romans, especially to give Rome a glorious past, and only some pivotal events are regarded as factual. The same goes for the
fasti, which are reliable after 367, and somewhat factual between 450 and 367. Everything before is most likely legendary. For example, the early
fasti (until around 480) are full of interpolations staging plebeian families who become important later on - but certainly weren't in the 5th century.
(Rome is supposed to have hosted three original tribes as well, but it's hard seeing what's part of a more or less genuine historicity, and what could come from a PIE tri-functionality (or non-functional triade) as much as genuine organisation.
As said above, there's no evidence for tripartition in ancient Roman society, and this particular three tribes = three functions theory ended up being abandoned by Dumezil himself.
The three tribes are certainly not Proto-Indo-European. Rainer considers the
curiae (from co-viria, associations of men; consider also
quirites) to be the original organization of the Roman state. Membership in the curiae was determined by affiliation to a
gens, instead of the territorial criterium used for the tribes. Also, the curiae had religious functions, while the tribes hadn't (AFAIK). The tribes were created only later to organize the Roman military (each tribe supplying 1,000 men). It is likely that the number of 30 curiae was permanently fixed when the tribes were instored -- the organization into three tribes and thirty curiae is obviously artificial. This is also reflected by the names of the curiae, who are sometimes named after gentes and sometimes after persons. Thus, the tribes weren't part of the primitive organization of Roman society, and could only have been established when the Roman state was already solidified.
We don't even know when the Roman kingdom fell, as records were destroyed with the Gallic sack of Rome. But the records we have are wrong, as conveniently, according to them Rome turned into a republic literally a year year before Athens, which means Rome can call itself the first democracy. It's a little too convenient.
Unlikely, given that the Republic wasn't actually a democracy as the ancients understood the term, and, far from calling themselves the first democracy, Romans generally looked down on Athenian-style constitutions for being too open to demagoguery and mob rule.
The point is that the Athenians got rid of their tyranny in 510, when the Spartans overthrew the tyrant Hippias. So it would have been tempting for a Roman historian to set the overthrow of the Roman monarchy* in 510/9, to make sure that Rome doesn't "rank behind" Athens. And the dating of the beginning of the republic is really quite conjectural. Bringmann writes that in 304 BCE, 204 nails were counted in the temple of Jupiter, so it was calculated that the temple had been dedicated in 509. The inscription on the temple mentionned Marcus Horatius Pulvillus, who had been
eponymous magistrate in 378, when the temple was renovated. Since M. Horatius accidentally shared his name with one of the mythical founders of the Republic, the Romans deduced that the Republic had been founded in 510/9 BCE.
However, it is likely that the Roman overthrew their last king around 500 BCE, even if the precise date is impossible to determine.
*You might object that the Romans overthrew their
king, while the Athenians did the same with their
tyrant. But some argue that the Roman Kingdom was a tyranny to some extent, at least if you consider the policies of the Etruscan kings. The mythical Servius Tullius replaced the curial and tribal organization of the military with the organization by centuries, thus weakening the power of the gentes and patres. This is in line with the common action of Greek tyrants, who underminded the rule of the aristocrats by strengthening the hoplites. Therefore, it's hardly surprising that the Romans despised the monarchy as much as the Greeks hated the tyranny.
The tale on both Tarquinus rise of the throne could be interpretated by meddling from neighbouring Etruscean cities on Rome, meddling that would have more or less annoyed Roman aristocracy. One could argue that there's as much mentions of fight between Etrusceans kings and their neighbours. Rightly so. But I think what could be relevant are the mentions of a treaty (treaties) passed with Etruscean cities.
The problem would be eventually less about having a foreigner as a king (which was common enough), but having someone that is not seen as incarnating the interests of one city on behalf of "foreign" people (which could be either newcomers into aristocracy or neighbours).
It's also worth considering just what an "Etruscan regime" or "Etruscan domination" would entail. The Etruscans, of course, weren't politically united, so if Rome was dominated by an external Etruscan polity this would presumably entail being made subject to a nearby Etruscan city-state. But Rome's size during this period was already enough to put it in the top tier of Italian cities, so it's unlikely that any other city would be strong enough to subjugate it for a full three generations. The other situation in which it would make sense to talk of an "Etruscan regime" would be if the Roman ruling class were deposed and replaced by Etruscans, who then formed the dominant power-group and confined native Romans to the lower classes. Needless to say, there's no evidence for such a situation, either in the ancient historians or in inscriptions or the archaeological record.
I think we can agree that even a politically disunited culture like the Etruscans can extert some form of "domination". In fact, the foundation of the Roman Republic took place in the context of the end of the Etruscan predomination in Italy. Aristodemus of Cumae had defeated Etruscan armies (led by Porsenna) twice; in 474, Hiero of Syracus defeated an Etruscan fleet at Cumae; the mountain tribes were gaining in importance, and in 424, the Samnites took Capua from the Etruscans. The Greek colony Cumae was conquered by the Oscans in 421. These events heavily limited the Etruscan influence in Latium and Campania, and might be the background of the beginning of the Roman Republic.
The precise reasons for the end of the Roman monarchy are uncertain, but conflicts between the Etruscan king (with an absolutistic conception of monarchy) and the
patres certainly played a role. Some also suspect that Tarquinius Superbus lost a war against a neighboring city. The Roman historiography assumed that Tarquinius and Porsenna were allies, but this is doubtful for at least two reasons: First, there are hints that Porsenna actually conquered Rome in 508, but he didn't restore Tarquinius to the throne (even if this was the mythical reasons for his war against Rome). Second, Tarquinius was later allied to Aristodemus of Cumae, an old enemy of Porsenna - Porsenna and Aristodemus fought against each other in 508, according to Roman historians. So you could imagine that Tarquinius lost a war against Porsenna, that Porsenna conquered Rome and that his triggered the end of the Roman monarchy.
Interestingly, if you look at the Fasti, the Romans elected consular tribunes for a lot of the years preceding 367. So maybe the progression was something like: the Republic started out with two magistrates, called praetors or consuls or possibly both, but over time they came to the conclusion that two magistrates weren't enough, and experimented with electing more praetors/consuls/consular tribunes instead. Later they came to the conclusion that this didn't work either (maybe having so many people with veto power over each other made it difficult to get things done? That's just speculation, though), so they decided to reinstitute the dual magistracy, but with a third person under them to take care of the city while the other two were away campaigning.
I just re-read Bleicken's book about the Roman Constitution (I hadn't done it for years) and I realized that I misrepresented his theories. As I wrote above, he is of the opinion that the first Roman magistrate was the Praetor Maximus, and that collegiality developed only quite late (compared to tradition). But he gives reasons for this, reasons that I omitted in the description of this theory. Again, this theory seems to be a favorite of germanophones historians, while English-speaking historians mostly reject it. Like I said, the proponents of this line of thought assume that the rex wasn't replaced by a dual supreme magistracy, but only by one
praetor maximus or
magister populi. This might be the successor of an older office, the magister populi, who had led the army during the monarchy. As stated above, the only source for the existence of a praetor maximus is the ambiguous law mentionned by Livy; but replacing the king by one magistrate, with a term limitted to one year (annuity), is more logical than instoring annuity and collegiality simultaneously. Also, the Roman army of the time was not so great that it would have needed two commanders.
The century following the end of the monarchy saw some experiments with the number of the supreme magistrates. According to Bleicken, the praetor maximus received two colleages, and this had two reasons: the patricians had to give plebeians acces to a major position, without taking the risk that a plebeian might become praetor maximus. Also, the Roman army had become to large that it was necessary to divide it into two legions, so that each of the
consules commanded one of it. After some time, the consuls became the more important part of the college (due to their military duties), and the former praetor maximus became the subordinate
praetor urbanus. Other historians take into consideration the existence of consular tribunes in the fasti. After 450, the praetores may have been replaced by Military Tribunes (the attribute with consular power was likely added by later historians, to distinguish them fron the Military Tribunes of their time), for two reasons: the wars on several fronts and the necessity to allow some plebeians to exert some office, without risking that a plebeian might become praetor maximus. Just that the Romans didn't return to their old order in 367 (as Roman historians assume), but that a new organization was created, with two consuls and one praetor urbanus.
To sum up, the point of the theory is that collegiality wasn't a consequence of the end of the monarchy, as tradition suggests. It became necessary only later, to manage the increased size of the Roman army, and to manage the settlement between patricians and plebeians (respectively, to prevent that plebeians seize power by administering the supreme magistracy (
praetura maxima)).The only direct impact of the overthrow of Tarquinius Superbus was annuity.
The existence of the dictatorship isn't really a counterargument, because the dictator was (originally) immune to provocation and to tribunician intercession. So even if a praetor maximus existed, a dictator could have been necessary at some times, because the praetor was subject to control by provocation and interecession. Only the dicator could exert truly unlimited power.