Volume of procedures is absolutely important! I asked an oral surgeon once this exact question and his response was that he'd let any oral surgeon operated on him who made jaw surgery a major part of his practice. He didn't give me a number but he emphasized the importance of recent procedures over the total number.
Short term volume is important to maintaining skills. Studies have compared surgery to playing video games, so much so that some surgeons actually play games before procedures to warm up. Ever play a video game, get really good at it, and then come back after not playing for a while? Sure, you have a good idea of what's going on and it may come back quickly but you need practice - recent practice - in particular to be great at a procedure. Operation time is critical to success, there's hundreds of steps, and you don't want a surgeon stumbling around because he's hazy.
Long term volume is important for better handling of corner cases. Surgeons who've done hundreds of procedures will have ironed out the common mistkaes. Surgeons who've done thousands of procedures will understand all the anatomic variants. Those who've been doing it a long time will have a better understanding of the fundamentals, the alternatives, the evolution of the procedure. That's nearly impossible to replace. Those with long term experience appreciate results, others have to settle for reading the text others wrote.
That aside, surgery is business and the more procedures a surgeon is doing, the more investment they can afford to make in improving it. That means subscribing to the latest crazy expensive journals, traveling to conferences, trying all the newest technologies, reading expanded textbooks, etc. I was just looking at oral surgery textbooks tonight. Your average surgeon receives about 100 pages of training material on oral surgery. Jaw surgery textbooks can be 10 times that length. He's not going to read all that unless he has good reason to. It's no wonder my local surgeon seems to lack a fundamental understanding of the etiology of my problems.
There are surgeons with high volume who are good but not great. High volume guarantees at least average performance and it is a necessary but not sufficient condition for great performance. The opposite can be said for low volume. What are the numbers? It seems that an average bad surgeon does 10/yr, an average good surgeon 50/yr, and a great surgeon 150-500/yr. That's 1/mo vs 1x/week vs 3-5x/week. A good surgeon has done at least a few hundred surgeries and a great surgeon has done a few thousand.
It should be noted not everyone needs a great surgeon. Many problems are simple to fix and a good local guy is sufficient. The trouble is, it can be hard to determine who is routine and who isn't. The patient certainly can't tell and it appears even orthodontists can't. The orthodontist in my city whose done the most adult surgical cases called my case "very routine", having only examined by teeth but never looking at my imaging. My dentist, by contrast, called my case very extreme. The next most experienced orthodontist I found, whose done hundreds of surgeries, has admitted that even he hasn't quite seen a case like mine yet. So if all these "professionals" can't agree on who's routine and who isn't, the only way for a patient to tell where they belong is to start by consulting the great guys and see what their opinion is. The sad reality of surgery