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.