Persia was happy leaving Greece independent because it wasn't that rich or prosperous despite what some people assume. The only prosperous places were Athens and Thebes and they were only 2 cities out of the 100's of Greek cities. In the 5th century BC, the richest and most prosperous lands were Egypt, Babylon, Media, Assyria, Lydia, North India, and the Caucasus. Persia took over all of these lands in addition to many others. It simply did not need Greece which was not rich in resources. Maintaining control of Greece also would have been too expensive because of its distance from Persia although Persia did maintain large potions of northern Greece and Thrace for a time, After the Ionian Revolt of 499 BC, the Persians and their king Darius wanted to conquer Greece more than ever. Persia wanted more and more land. Also, the Greeks had helped the Ionians to revolt against the Persians, and had marched to Sardis and burned the city, King Darius felt the need to conquer all surrounding nations that weren't his.
Kind of long but i hope this helps!
