Soldato
Some of them, yes, but not usually at will unless they were wealthy. For example, a sailor on a merchant's trading ship might be well travelled, even abroad (there was a lot of international trade), but they wouldn't be travelling where they chose when they chose. Although they might well get some time spare in a trading port, which would probably be at least a fair sized town (by the standards of the time, when a few thousand people was a big city) with a dentist.
We've had this conversation before. The Crusades involved large numbers of people travelling very far afield. You could easily have someone or several someones in a medieval village who had been to Spain or even Jerusalem. Port cities like London saw large volumes of foreign trade. Then there were regional wars meaning many people had travelled across some quite wide ranges of the land. The popular image of a medieval village is that the people there are born, die and have little awareness of the outside world. The reality was that people were far more travelled than most expect. I don't know why you feel the need to try and contradict that. It's well established.
True, but how often would one be stopping at or near your village?
They'd probably stop at the nearest town quite often, actually. And most villages had very close connections to their nearest town - farmers and traders would travel there often.
Maybe, although it would be better for their business to not do so. A dentist who could pull teeth efficiently and with as little pain as possible could charge more and would probably get more work too. People tend to prefer to be good at their trade, anyway. But medical knowledge in medieval England (or anywhere else at the time) was quite limited. There would be a risk of infection and treatments to prevent or treat it were of limited effectiveness. Also, as you say, cost was a factor. Pay for the dentist, probably pay for somewhere to stay overnight, probably pay for some sort of aftercare product that you hope will prevent infection (and might - some plants do have antibacterial properties)...it was coin you would probably prefer to spend on something else (assuming you had they money). Oh, and pay for the booze to get drunk enough to dull the pain There might be other forms of painkiller available, but alcohol would probably be cheaper and safer.
I was making a joke based on the popular image of dentists.