It's really that simple? That's . . . actually incredibly baffling.
Really? Why baffling? The idea that you and I, who live together, should treat each other as we want to be treated, seems rather natural, and so does the idea that when there`s a conflict, the party which has more angry men on their side would prevail over the minority (a very broken-down understanding of democracy=popular rule). Now of course the idea that some people - especially those with more experience, a large cohesive family, achievements, wealth etc. - will be more listened to than, say, dim-witted orphan teenage boys, is also rather deep-rooted. If you look at pre-civilised societies, you`ll find proto-democratic and proto-aristocratic elements often combined. What you don´t find there and what only came up in complex societies is the extreme centralisation of a monarchy and divine kingship.
The detailed picture is, of course, more differentiated. Firstly because of the tendencies of oligarchisation already mentioned. And secondly because the republics you alluded to emerged in different contexts and from different historical traditions.
In Classical Greece, poleis were "constitutional" from far before Kleisthenes, in the sense that they combined elements of various strands of political customs into intricate political systems. They balanced out the interests of yeomen farmers and merchant oligarchies. As society changed, so did these constitutions, and the Athenian example is not a singulary phenomenon, only the best documented and most powerful one situated rather at one end of a wide spectrum. To pre-Alexandrian Greeks, the idea you consider more natural was abhorrent: "tyranneia". Tyranneia was rejected not only by Athenians; Thebans, Spartans etc. likewise abhorred it, or so did at least the philosophers we`re basing our historical picture on. A somewhat similar picture could be drawn for the Punics.
In Rome, the res publica evolved from tribal traditions into a constitutional model, too, perhaps under Hellenic influence, and here, too, the idea of a monarchic "rex" enjoying absolute or even divine power was abhorred, too, for many centuries. Now of course the Roman Republic expanded so far that it needed a degree of centralisation and militarisation which, combined, simply blew up the republican constitution. Mark that the Principate was, on the central level, a de facto monarchy, but on the local levels, which did most of the day to day politics, oligarchic structures continued unabated.
In India, early republican structures emerged from a constitutionalisation of tribal traditions, too. What eliminated them, from the Gupta age onwards, was a segmentarisation of oligarchised republican customs into separately acting "jati" (castes? guilds? difficult to say for that age), which was easy to be overarched by a mandala system of feudal military rulers above - or beside - it.
Among the Germanic and Slavic peoples, (first ritual, then military) kingship combined for centuries with democratic assemblies (Things, Veches) where conflicts were resolved and common decisions were taken. Now, these were tribal structures. The reason why they developed into feudalist ones is the heavy Late Roman influence.
Republican structures - a broad umbrella term anyway - emerged almost everywhere in the world, although there were times when they were more prevalent and others when this was less so, and there were regions with less republican traditions (China, Egypt) and others with more (Europe, India). Their legitimacy was never generally or universally questioned as such. It derived from local traditions, both orally transmitted and fixed in written constitutions, and was elaborated on by philosophers. The same goes for the divine kingship you portrayed as a counterpart, too, of course.