That's a very strange outcome indeed, I wonder if you could have pushed for it anyway. My wisdom teeth were also impacted (nearly buried in gums, horizontally aligned), and I also opted for a local anesthetic.
The worst part of the procedure was seeing the size of the syringe. They really didn't spare any anesthetic for it. I felt numb all the way to my neck and ears. To my surprise the whole procedure took less than 40 minutes from start to finish, including cutting the gums, sawing the impacted teeth in half (the noise and smell is not for the faint of heart), and then putting sutures in.
Personally, I don't regret getting rid of them either. Made hygiene slightly easier and no risk of inflammation where the wisdom teeth were breaking through the skin.
Working in a dentist's office, I have seen a wide range of tolerances for discomfort (not pain: we always anesthetize). The people who need ativan or nitrous for a simple filling are probably going to need general for impacted third molars. Those need to be sectioned if they're going to come out without breaking the jaw. In USA, relatively few dentists would offer general anesthesia in a non-hospital setting.
local anesthetic to the jaw or maxilla is just incredibly effective
After calculating the number of hours of work the anesthetic would cost me, I decided to bite the bullet of go with a local anesthetic. (My dad was also tough-guying me to skip the general anesthetic.) So I called the surgeon's office to make an appointment. When I mentioned that I would be opting opt of general anesthetic, the receptionist paused and asked me to hold. When she came back, she said that the doctor specified that general anesthetic would be necessary. I mentioned the conversation I had already had with him. She again asked me to hold. When she returned, she said it was no longer an option.
I put off the appointment. Miffed, I decided to take a closer look at the practice. This was pre-internet so I went to my local public library. I tracked down a British NHS study that suggested extraction was over-prescribed in the US in part due to the private insurance system. (I guess you can insert your tired joke about British teeth here.) One NHS study coupled with my incipient suspicion of the American medical system was enough for me. Plus all the money I was going to save. I decided to forego the surgery.
Almost 30 years on and I can say I have no regrets. (Yet?) My third molars are still buried in my gums. A few years ago, the bottom right one partially broke through the gum. It was irritating at times but never really painful. I take care to floss and brush it with my other teeth. It seems to have come to rest. If I remember correctly, the study stated that after age 30 or 40, most people's wisdom teeth will have settled.
One internet commenter's tale backed by one study for which I no longer have the reference.