dresali: I grant you that if there is a drawish move for black that a swap rule could "work" (although that would be a very different game, one that is decided on the first move). But it's not at all clear to me that, for any first move of white, there is such a move for black. Not that I really like games where blacks first move has to be a bad one.

As for your perfect information example, I'm a bit confused about your meaning of 'good' and 'mediocre'. Since all moves of white (A, B, C) can be beaten (A', B', C') and alternatively lead to a draw (X), I wouldn't qualify them as "good" moves. Although I guess that if white doesn't have any moves available that win, all moves are equally "good".

I still claim such a game would be a game of perfect information (nothing is hidden or determined by a dice roll). But I'm fine with you seeing it differently.