The US loves to sedate. You guys get absolutely blasted when you have your wisdom teeth removed. In most of Europe you get strong pill painkillers for the first few days and then it’s paracetamol.
I don't know if you're expressing a common misconception here, but a lot of Americans also think general anaesthetic is widely used for wisdom teeth removal, and it isn't. What is widely used is deep sedation, a combination of ketamine and benzos which keeps the patient calm and, the nice part, prevents any memories of the event from forming. It's maybe an extra hour of recovery, same-day procedure in either case.
Post-care is a few day's worth of entry-level painkillers unless the patient gets a dry socket. We use acetaminophen for post-treatment rather than paracetamol, since it's better (never understood the British obsession with that stuff, it's nasty business).
Anywhere else I would walk away from a terrible joke like that, but this is HN. I'm joking.
It depends on the situation. I had all of mine out this past weekend (in the US) and, because they were fully grown in, all they had to do was some local anaesthetic (about 8 shots around various parts of the mouth), wait 15 minutes, and loosen/pull them all. Total procedure was less than 30 minute and no painkillers prescribed after the fact.