I do (I rarely sit). But most times the surgeon is working, and does not notice my (at least) hourly presence (there are few cases that require my continuous presence). And during induction and emergence, God forbid to actually seem to direct/micromanage the CRNA, because that results in bad feelings from those, and they are contagious (you piss off one, you'll start noticing difficulties with others). So you stand there as the firefighter, ready to help the CRNAs when they frack up, trying to pick your battles and enforce the really important stuff (e.g. not extubating the morbidly obese in stage II). So what the surgeon sees is an anesthesia attending mostly just being physically present, maybe pushing drugs and giving some instructions, listening for breath sounds etc., but nothing like when supervising a resident. Unless they see you in a rare crisis situation, they don't see a big difference between you and the CRNA, because they don't see what's behind the curtains, they rarely hear when you discuss the plan (except when you have something to ask them to do differently - which they usually don't like) etc.
Anesthesia is the wizard of Oz for most people not involved. Hence they don't know crap about what really happens, and it's mostly a matter of artistic impression on our part. It's a good specialty for people who could have made a career in sales, not so much for the introverted, thorough, anal ones. The latter should just friggin stay in internal medicine.
