Why can't Edward get back his power to do alchemy? Roy Mustang's vision was restored, so why can't Edward Elric try to use something to exchange back his gate, like using another philosopher's stone? Is it that he didn't need alchemy anymore because he fulfilled his wishes?
Edward's actions when he recovers Alphonse indicate that he probably would not want to get his alchemy back, much less do so by using a philosopher's stone.


Ling offers Edward a philosopher's stone to use to recover Alphonse. Edward refuses because he and Alphonse had promised not to use a philosopher's stone (and more generally, human lives) to restore their bodies. Alchemy is surely less important than Alphonse is to Edward, so he would not want to use a philosopher's stone for recovering his alchemy (were it possible).
Edward tells Truth that he will be fine without his alchemy: he has always been an ordinary person who was not able to achieve everything he wanted, and even without alchemy, he has his friends. Edward accepts this result, so it would be unlikely for him to want to reverse it.


More generally, exchanging something for one's gate would probably count as a transmutation of sorts. If someone already gave up his ability to do alchemy, it would then seem contradictory for him to be able to exchange it back. (It is unclear whether another alchemist could initiate the exchange, but it seems unlikely in light of the personal nature of the gate.)