Can you allow me to reverse my answers? I hope to point it's for good reasons.
Among other things, there's no indication in the sources that the three tribes had different roles or functions, and some indications (e.g., the fact that they all had to provide soldiers) that they didn't.
O'm not really sure you understood my point.
When I said I think it could be as well tri-functionalism than genuine original organisation, I meant it. Not everything in a myth can be traced back to the former.
That said, you have some traces of what could be tri-functionality in the historical myth.
The founder deity/king organising the original society into three distinct bodies (after having searched support from divinities), whom generic name could be related to a variant on "three".
For such a basic foundation on distinct bodies to revolve about three can't be pulled away, when we know that the triads aren't limited to tri-functionalism in IE mythical organisation, but one should consider with more caution the triadic mentions when they can be relevant (Meaning in an important context enough : such as "three raven being seen together is a bad sign" or "three tribes organised with divine avail")
I would point, eventually, that I didn't even pretended even for one second that these tribes had different functions, but that they could have been
identified with different functions, more or less totemically (is that a word in english) and such in a real ancient part of Roman history.
Without entering too much in details, it have been advanced that Tites would have been associated with reproduction, Luceres with fighting and Ramnes with political/religious.
It's essentially based on the traditional ethnic division of the tribes, respectivly Sabins of Tatius, Latins of Romulus and Remus, Etrusceans of Lucumon.
These groups are often attributed some caracteristics (Propercius, but on Virgil as well, but it's a long time since I checked,so you'd allow me a possible mistake) : Sabins with their cattle, Etrusceans with their military skills, Latins with the political (and obviously) religious supremacy.
I'm not going to pretend that it couldn't be criticized (even if what is criticized is often an hypothesis made by Dumézil that he abandoned eventually, about these tribes BEING agricultors, fighters, etc.), but in a context of heavy mythification on first roman kings, you'd admit that there's room for including these.
Admittedly, I could have been quick on this for being more clearly understood. (but it wasn't, arguably, the subject at hand), but I think you're putting away too much things in your own answer.
so there's no real reason to think that the Romans would have seen anything wrong in having an Etruscan ruler.
I'm less talking about national identity in a modern sense, than a "national" dynasty; and less "Romans" as a whole than its aristocracy.
Rome, as an independent city, could less tolerate attempts againt its regional hegemony over Latins from the powerful Etrusceans that while far from being united, represented a political threat as in possibly limitating Roman power or even structures (Tarquinus expansion of centuries' tradition can be easily interpretated as a way to bypass Roman aristocracy power from Etrusco-Latins rulers).
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.
You'll 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.
Basically my point is less about having a foreigner as a king, but having someone that is not seen as incarnating the interests of one city on behalf of "foreign" people (which could be either new comers into aristocracy; or neighbours).
Am I clearer?