Would be nifty if non-party leaders could still select a game, but rather than starting it immediately they get the option to either (a) leave the party to launch the game solo, or (b) suggest it to the party leader (who then sees it as a notification of some sort and can start the game for everyone from there).
Minor things, but the former option would make it painless to try out new games without manually leaving your party first, and the latter would save some faffing about with one person saying "oh we should play this game" and the leader having to look it up manually.