In many of these cases, the city was sited in a particularly good location. Take Wilusa/Troy. It was sited near the Dardanelles giving it the ability to control and profit off of trade between the Aegean and Black seas. It had farmable lands, good sources of water, and a highly defensible citadel area. It is no surprise that a dozen or so cities were built successively on the site. It's an excellent place to build a city.

Athens was in a similar situation. Although the Persians razed the city, most of the people survived. They had to live somewhere. And there was an excellent city site right there. The Acropolis was a great defensive position. It was near a good port. There was good farming land nearby. There was a reliable water source. And the city was well positioned to dominate and control the rest of Attica including the silver mines. Plus there was a lot of stone and other building material that the Persians left laying about. For the survivors on Salamis, even disregarding the emotional ties to the old city site, there was no better city site anywhere nearby.

Once reestablished it is no surprise that it quickly reestablished control over Attica. Most of the legal claims to land, farms and mines, were held by Athenians. Athens was the most populous polis in the area. And quickly became so again after being rebuilt. So they had legal claims to the area and the men (and allies) to enforce their claims. Really there was no significant opposition. So the claims didn't have to be enforced at all.