As much as I love Wimbledon, I can foresee a day when all the coverage (aside from the highlights and finals) is on the red button. Indeed, I don't see why that shouldn't apply for other sports as well, including the Football World Cup, Olympics, and Commonwealth Games (to name but a few). In fact, I could argue that this could be extended to other events that currently aren't broadcast. So, sticking with tennis for now, you would be able to broadcast all of the other Grand Slams on the red button without affecting the trash that's currently shown in the afternoon. Even at the moment, there are several courts on display via the red button (the main channel covers one court, but you can often get other matches on the other courts by pressing the red button).
In all fairness, only very rarely do they ever broadcast Wimbledon on both BBC1 and BBC2 simultaneously (and only for a few seconds/minutes at that).