Suppose that Athens avoids the Sicilian Expedition, thus prevailing with its Delian League intact following a shorter Peloponnesian War; that in later years is only overshadowed as a maritime power by a polis adopting a similar government; and that this democratic hegemony lasts at least four centuries following the PoD (or to the end of OTL's "BCE") -- and JTBC, I'm only looking at the effects of this, not the how (there are
threads and TLs on that).
What would the Mediterranean (and surrounding) societies and polities look like in this time -- would it remain more balkanized into polis', or could larger proto-states emerge? What are the chances that any of the powerful full-fledged democracies (Athens, Syracuse, if it survives, etc) might expand their rolls of voting citizens, be they with the metics, the citizen women, or what have you? How would political (and perhaps general) philosophy be altered? And how else might western civilization be fundamentally changed?
I'll try my hand at answering this.
First off, it's my opinion that a supposed Athenian Hegemony would fall fairly quickly after a victorious Peloponnesian War (whether due to a victorious Sicilian Campaign, or luckier breaks in either Mantinea or Delium, or no plague, or something else), fairly quickly meaning not more than 50-60 years (though I do think it would last longer than Sparta's Hegemony IOTL), and certainly not the four hundred you desire. Athens was too heavy handed in how it dealt with its allies/subjects. They were already widely considered "the bad guys" in the war in large part because of how large their indemnities were upon the League, that largely went to make Athens better rather than improve the standing of the League or democracies in general. Trying to maintain this would have been futile over the long term; there'd be a large (and probably oligarchic and Theban-led) uprising against the Athenians, that would have the full support of the Achaemenids, and would be too big for Athens to contain.
As for how things would work... certainly, I think under Athenian rule, you'd see the subjects divided into poleis, but once Athens falls from power (or whenever a Greek polis cannot assert its hegemony across the Greek world), I think you start seeing Leagues more like those of the third century BC... stronger and more regional leagues, like the Achaean and Aetolian Leagues, that I guess could be considered sort of proto-states. I hope I answered that... wasn't quite sure how to answer it.
Culturally... I do think you'll see more great writers and philosophers, and I think you'll see more great architecture and whatnot like the Parthenon in an Athenian-dominated post-Peloponnesian War classical world. Democracies do tend to produce great philosophers/art/theater/whatever at a higher rate than the alternatives; the Italian renaissance and OTL's Athenian Golden age being the classic examples for those believing in that sort of thing (which, obviously, I myself am with, albeit somewhat tentatively). I have a harder time seeing voting roles increased (in part because they were pretty radical for the standards of the day already), especially for citizen women - seriously, ancient Athens wasn't exactly kind to women, even for the standards of its time.
As for how western civilization might fundamentally be changed... I'm not sure. Democracy might be even more discredited for even longer if Athens is seen as a really terrible and despotic empire, that takes from those it can to build itself up (this being the view of the states that defeated the hypothetical Athenian Hegemony); but, on the other hand, it might be more readily accepted earlier in history, due to Athens' greater direct influence on the world. It certainly doesn't mean that
liberal democracy is going to do better though.
Probably!why not? the Western Asia Minor cities in their majority exceeded that number.Don't forget that these cities raised a revolt against the Persian empire and nearly succeeded! ditto for Corfu,Amphipolis,Lesbos,Chios,Samos, Thassos etc most of them maintaining fleets exceeding 100 triremes.
I don't think anyone would argue that there were several cities/communities within the Delian Empire whose population numbered over 100,000, or even a few significantly over that mark. However, to say that the average population for all of the states of the Delian League was over that mark... is frankly absurd. I would believe that the total population of the Delian League's members is somewhere between 10 and 12 million people, considering how large some of the Ionian cities and Athens itself was. But 20 million is an extremely high number. Consider that all of France only reached 20 million people in the 17th century; consider that the United States currently has 285 cities populated over 100,000 people, the level at which you argue that 176 ancient Greek city states averaged over 2500 years ago. It seems very unlikely without a lot more evidence to back that up.
EDIT: Sharkani Rend did a much better job countering this than I did.