For chess, the future possibilities are so vast, you can't call them "perfect knowledge" with a straight face.

This is not what the terminology "perfect knowledge" means. Perfect knowledge (more often called "perfect information") refers to games in which all parts of the game state are accessible to every other player. In theory, any player in the game has access to all information contained in every game state up to the present and can extrapolate possible forward states. Chess is a very good example of a game of perfect information, because the two players can readily observe the entire board and each other's moves.

A good example of a game of imperfect information is poker, because players have a private hand which is known only to them. Whereas all possible future states of a chess game can be narrowed down according to the current game state, the fundamental uncertainty of poker means there is a combinatorial explosion involved in predicting future states. There's also the element of chance in poker, which further muddies the waters.

Board games are often (but not always) games of perfect and complete information. Card games are typically games of imperfect and complete information. This latter term, "complete information", means that even if not all of the game state is public, the intrinsic rules and structure of the game are public. Both chess and poker are complete, because we know the rules, win conditions and incentives for all players.

This is all to say that games of perfect information are relatively easy for a computer to win, while games of imperfect information are harder. And of course, games of incomplete information can be much more difficult :)

A human might not be able to, but a computer can. Isn't the explicit reason research shifted to using Go the fact that you can't just number crunch your way through it?

AlphaGo Zero did precisely that. Most of its computations were done on a huge array of GPUs. The problem with Go is that look-ahead is more of a problem than in Chess, as Go has roughly between five and ten times as many possible moves at each point in the game. So Go was more of a challenge, and master-level play was only made possible by advances in computer hardware.

Chess was already easy for computers. That's why Arimaa came to be.