From a selfish, personal standpoint, I would love to see shows have different schedules, with matinees on different days and different days off. As a theater tourist, it would allow me to see more shows, or god forbid, take a night off and see a few more matinees instead. For this upcoming trip in June, Miss Saigon was the very first show I locked in, because they have a Monday night performance while I'm in town. It was the only show, so that made it really easy to commit.
A Friday matinee would be great, but the poor actors who'd have to do 2 shows on 2 consecutive days. That sounds grueling.
Does London really do different schedules? I was just there this past weekend, and I couldn't really find anything that played a Sunday matinee. The traditional dark day in London is Sunday, which I find a bit annoying, to be honest. When taking a long weekend for a trip you *have* to take Friday off and make the the trip Fri-Sun and deal with a ridiculous crowd on the airport (it was't pretty). If there were shows on Sunday, I could make it Sat-Mon and still see the same amount of shows, but be a little off schedule with other weekend travelers... But I'm going off-topic, sorry.