That might be another difference between him and Sinatra, then.
Sinatra (who I did see live, on a very good night in 1982, at Caesar's)...of course there was "show biz", but ultimately it was Sinatra, period. He was more/bigger than any one thing.
I went to the show because I had a chance to go, period. Wasn't really expecting anything, but left totally freaked out, it was SINATRA by God. If I hadn't seen, I would not have believed it.
I might well have responded to Bennet the same way, possibly even more since he worked with his trio, right? Sinatra had a big band and did a few songs with rhythm quartet, but I was expecting to hear a bunch of schlock with sappy strings, so that just added to the surprise. But ultimately it was just Sinatra's sheer power of skill (and his skill of power) that shook me up.
I have no doubt that Bennett live would have done the same thing in his own personal way.