I do it because the instructions say to. IMO, there's a reason the companies direct you to wait, and there's a reason some formulas require a 24h cure, and some can be instant use. If you want immediate use, get the Permatex Great Stuff 1 minute gasket maker. If you don't mind waiting, use the Permatex Ultra line.
Companies like Permatex pay people a lot of money to develop their products. There's a reason they have different products with different cure times - and they're NOT the same thing in different packaging. If you want to know the why, email them. If you don't care about the directions, then do what you've always done, what your dad did/does, what you were taught, etc.
As to the example from the FSM, that was most likely written several years ago. Products change a lot, and those directions may not be applicable to the "latest & greatest" in RTV gasket options. Also it does specifically reference Mopar RTV & similar products. I've never used Mopar RTV, but I'm assuming it's a different formula than the Permatex formulas being referenced in this thread.