EJ – Good one! I’m going to assume we’re talking about full-fledged crossovers and not continuity nods, since the latter are some of the most wonderful things in all of televised entertainment, especially when they link shows to the Tommy Westphall Multiverse.
I’m no historian, but I assume the earliest crossovers were a way to tell people that “Hey, this other show exists!” They didn’t have the entertainment culture that we have, so when Danny Thomas popped up in character on I Love Lucy, it was to let viewers know that there was a thing called The Danny Thomas Show, and they might like to watch it.