I don't particularly like dentists and I was offered a root canal, but decided to just have the tooth out (lot less time and pain) and as it was on the side of the mouth, doesn't really show anyway.
As for getting into the dental hospital, it is possible that you have to be referred, but I'm not sure. I know my friend is scared to death of injections and she has to be put out to have anything done, so she goes to the dental hospital. I don't think many dentists actually put you out anymore.
Our dental hospital is purely that, and not a normal hospital. They teach students there etc. Presumably it's the same everywhere. I suppose its a specialised treatment, same as eye hospitals.