Interestingly, you're probably awake for more than 3 seconds but experience propofol-amnesia. At least, I did: I spoke with my surgeon in post-op (and said embarrassing things) and he shared with me some other embarrassing things I'd said after I "blacked out" (count back from 10).
The amnesia was considered a benefit because it's not the case that you want to remember everything that happens immediately before surgery...
Both times I had surgery, I only remember counting down to maybe 7 while laying down, then waking up somewhere else entirely in a wheelchair, with no idea of how much time had passed in between. I wasn't told about things I might have said, embarrassing or not, either at the beginning or at the end. I hope I'll never get to ask for staff to make a mental note next time.
My ex, waking up from anesthesia, heard the surgeon chat to others about $chain (local supermarket), to which she yelled out of the blue, to their surprise and amusement, just "$chain sucks!". She had no recollection of that and only knows about it because they told her later. [The place is ridiculously expensive, worse than Whole Foods was before the Amazon acquisition.]
The amnesia was considered a benefit because it's not the case that you want to remember everything that happens immediately before surgery...