I can not give an in-depth answer regarding to Athens or Carthage, or the Etruscans even, but I can tell you what Tim Cornell in his The Beginnings of Rome writes about the regime change in Rome at the turn of the VIth century.

So, the background according to him that your suspicions are well-grounded, at least in the case of Rome, the revolution(?) was part of a wider upheaval in Italy. It was a time when powerful warlords with their personal armies wrought constant changes on the political landscape in Central Italy.

That said we don't know for sure what happened (yet). Luckily there is certainly no lack of conjectures whether you want to hear antique or modern theories.

As you noted, the literary tradition is that the aristocratic revolution in Rome was direct response to abuse of power. Cornell thinks that it is a plausible scenario, but at least the amount of fighting involved is probably underestimated in the traditional narrative, because archeology attests that the city of Rome suffered heavy damage at the turn of the VIth century.

An also attractive theory is that Brutus and Tarquinius Collatinus were making a coup d'êtat. They didn't intend to abolish the monarchy, they wanted to take it over. But Collatinus was forced to leave Rome (maybe the machinations of Brutus) and Brutus perished, so the aristocrats filled in the power vacuum and set up an oligarchic government.

An other theory, which was already suggested by antique historians, is that Lars Porsenna was not some bystander who got later involved at the request of the deposed Superbus, but he was the one actually deposing him, and the early consuls were the leaders of the puppet-government he set up.

In an other (modern) narrative the whole annalist tradition is labelled as historical fiction, and it is proposed that the monarchy was slowly phased out and in the course of generations it was replaced by an oligarchic government.

Cornell doesn't have a personal theory about the exact sequence of events to conclude with, but he thinks there are some things which need to be pointed out.

First, the monarchy at the end of the VIth century is almost certainly not the elective monarchy of the earlier ages. The last king who was elected by due process according to the tradition is Tarquinius Priscus, both Servius Tullius and Tarquinius Superbus came into power by coup d'etat, and maintained their hold on power by the force of arms. It is also possible that Servius and Superbus weren't kings in name, and the elected kings were kept around as figureheads. The office of rex sacrorum, usually thought to be a republican invention, might actually be a much earlier development. Such twofold monarchies, where there is a monarch with sacral, and one other with political power, are actually quite numerous in history, so this at least is not an unbelievable conjecture.

Now on the consuls. The office of consuls (who were actually called praetors in the beginning, because of course they were (ㆆ_ㆆ) ), or something like it existed in the monarchy, they were the commanders of the classis, the hoplite army of ancient Rome. It is even possible that they were elected by the classis. Maybe this proto-republican institution was really just used to fill a power vacuum after the tyrants were removed? Maybe there was a new and more powerful institution created, modelled on the old one?

Then it is also worth pointing out that the age of tyrants did not necessarily end with the monarchy, the Sabine Attus Clausus, the forefather of the powerful gens Claudia may have been just an other powerful aristocrat, but he also may have been the absolute ruler of Rome for a while according to what we know.

Also worth noting that the revolution of 450-449 is supposedly kicked off by a conspicuously similar story than that of Lucretia: the tyrannical Appius Claudius tries to rape Verginia, she is killed by her father to save her from the shame, and then the secession to the Aventine.

Now, to close this garbled mess of an answer, you are, again, right suspecting that something was up in the air at the end of the VIth century, at least in Italy. It was an age when regimes were toppled even in the biggest cities in the region, and powerful adventurers/aristocats, or a group of them could seize power if they were lucky enough. That said what is the exact relationship between the changes in the different cities? Who knows? We only have conjectures about what happened in the first place.