I think players should be able to rate a beatmap after a multiplayer game, that will make things easier. If I played a terrible beatmap in multiplayer game, I won't want to go back and play it again just to rate it.
This can apply to rating a beatmap after closing the score panel (just used to do it so fast, it is easy to skip that part and forget you wanted to vote).
Proposal : Rating a beatmap should be available for any beatmap on which your play count is greater than 0 (you played at least once).
To some extends, this is also a cheap way to solve the mp suggestion.