Uhhhhhhh.....no, I didn't miss the point at all, I promise. I understand exactly what you're talking about. I just think it's silly.
Ran it by a couple of my LA Co. SD friends this morning, and they agree. They said the absolute dumbest thing you can ever do in a mayday situation is change channels, when you are on a channel where you know people are hearing you. It's the reason their pursuits are covered on whatever channel you happen to be on, including the main dispatch channel, and other resources are patched in if necessary. Because it's stupid to change channels in a situation like that.
They agree that it's useful for finding the dispatch channel (i.e. Channel 1), for example, but if they are in a situation where they are going to be switching channels, they can simply look at their radio.