I've noticed that 99% of blitz players do not. Still not many classical players join in for some post mortem, but they're much more likely to if I invite them.
I myself analyze 95% of my blitz/classical games with a computer. I think the only time I analyze myself is if I try a game blindfolded or something.
I do a slight analysis Lichess . The computer always has better moves. I try to memorize all the recommended moves and replay the match copying the computer moves.
I analyze every classical game shortly after and for a longer amount of time later that day. I don't think immediately using the computer to analyze is a good idea though, unless you already noted where you think you went wrong.
Personally, I immediately analyse, when something have bothered or excited me during the game. Its always a lichess analysis (I really dont need more than it already gives and its SO FAST...)
Wierdly enough, I don't like it, when the other player stays for analysis to complete as well... :D Does anyone else wanna be alone in the analysis room ? :D
i feed every game thats blitz or longer to the computer. served me well so far