A worse idea, but still better than the status quo, would be for the "draw" functionality to also check the previous position, like it does on FICS, in case of an opponent's move.
I make the move Re1, which generates a 3-fold repetition.
I navigate to find the "draw" button. This takes forever, of course, so in the meantime my opponent makes a move which breaks the repetition.
When I finally find the draw button, the server can be changed to recognize repetition positions from when it was my move also.
Please, please, please. When playing a game, why not have the letter 'd' be a hotkey for offer/claim a draw? It is so slow during a game to navigate away from the board to find the draw button.
It's very fast, and would be welcome.