What do we mean when we say it today?
Nowadays, we use "too much of a good thing" to talk about excess. Too much chocolate or vacation might actually be bad for you, even though those are good things. (Although we've yet to see too much of either of those things. It's chocolate, for crying out loud.)
We bet most of the people saying this one have no clue the double entendre behind "thing." This is one joke that's actually gotten tamer over the years.