[Xhad]

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What does raising on the flop accomplish?

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Mostly freecarding, with a side of outs buying and it's not impossible our hand is good. All he did was pfr from a mid position and make a possible cbet, many high card hands including worse As are still in his range.

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Is the problem with the river raise that there's no upside to it?

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Sorta. Basically:

-I assume BB never folds this river. He probably calls if your hand is good and raises if it's not. So you lose 2/3 bets when behind to him (depending on if you were folding to a 3bet) and win 1 extra if ahead.
-Given how button played this hand he usually either has a made hand worse than yours, worse hearts or occasionally something like Q9 that made 2 pair. He's basically always raising 2pair and folding busted hearts. The most important part is that something like A9 can probably fold the river for 2 cold but will probably overcall if it got this far. If you raise and get 3bet that's similarly bad to raising BB when he has you beat, except it's easier to fold to a 3bet

So basically raising is only better when you have BB beat AND button has busted hearts. If you're beat by either player calling is obviously better, and if you have BB beat and button has a made hand then you're still getting the same 2BB you would have gotten if you raised.