Are they not? MoGo beat pros of 9 Dan on 9x9 in 2011: https://www.lri.fr/~teytaud/mogo.html
Fuego beat a pro in 2008 using MCTS actually.
Not sure what you meant regarding MCTS, I never said anything about MCTS not being able to beat pros.
See, a chess program needs to find a lot of valid moves (see Deep Blue which won because it had stupid but extremely fast HW move generators), evaluate the moves and do a very deep search, up to 14, out of the very few alternatives. Russian chess programmers were better those times. They came up with AVL trees e.g. But hardware won.
In Go it's completely different. A move generator makes no sense at all, and a depth search of 14 neither. There are not a few alternatives, there are too many. What you need is a good overall pattern matching of areas of interest and an evaluation of those areas. And we saw that this feature outplayed Lee Sedol. Sedol couldn't quite follow in the recalculation of the areas.
Same as in chess AlphaGo learned the easy thing, that the center is more important than the corners, something Lee forgot during the game. But it's not a deep search, it's a very broad search, and very complicated evaluation function. A neural net is perfect for this function.
> whereas in Go no such function seems to exist.
It does exist. It's the neural net. It's a simple pattern recognizer, which learns over time more and more.
Evaluation function exists but it is not as simple as it can be for chess.