I've just been reading the Muddy Waters biography-The Mojo Man-by Sandra B. Tooze . . . It seems that, by the time Muddy was established(in his mid-forties-in is regular Chicago club dates), he'd let the band play each SET by themselves, and only join them for the last number of each set. It appears as if he felt that he had earned the "down" time, and this way (in his mind anyway)he could go all out on the songs he DID sing . . .
I bring this up only to point out that, perhaps, the late entrance originated from this period in Muddy Water's career . . . Most "traditions" within a tradition start from emulating the style of one of the "founders" . . .
As far as Joe's comments about playing to audiences . . .
I can only speak for myself, but I've found it plain "necessary" to keep playing in front of audiences. I've gone for 4-5 years at a time just doing studio work, or practicing, but sooner or later I've had to go back out and see "what I've got" by going back out in front of the public. Sure, there have been times when I've found myself out late, away from my family, in a place I didn't particularly care to be, but(for me), to continue to improve and grow as a player, I've had to go out and deal with playing in front of people.
Also, I've found that there are levels of playing(again for me)that just don't happen unless it's in the heat of the moment-and it's the interaction with the crowd that pushes you there . . .