I agree with
@LucidSplash and to add a few thoughts...
When considering a residency, two things matter above all else. #1 Pathology, #2 Mentorship. You need both in order to graduate from the program and be in a well trained physician. This is true in ALL specialties, not just surgery. In surgery, pathology means cases. Both operative and non-operative. You have to see a large volume of patients over an extended period of time. This is not just about technical skills. This is about acquiring experience to be a safe and effective surgeon. Yes, you need to do enough operations to be technically competent, but you also need to learn which operations to pick when there are options and even more importantly when NOT to operate. But, pathology alone is not enough. You need surgeon mentorship in order to excel. You need staff surgeons to teach you how to manage the pathology, pre-op, in the OR and post-op. If you don't have staff willing to teach and mentor you, you will not learn. If you don't have staff willing to sacrifice their time and energy to train you, you will not learn. Part of that means a certain amount of level appropriate autonomy. If you don't get increasing amount of rope to work with, you will not progress nearly as much.
It is also important to note that not all volume is equal. Excessive service requirements from busy, but poorly mentored services can really kill a residency. Sometimes it can be a trauma service, but more often than not it is a super private, busy niche service that simply absorbs resident time, but does not afford them training.
At the end of the day, volume is not everything, but it is a huge component of your training. There is certainly a limit and there are malignant programs out there, but you need a lot of cases to really get ramped up for going into practice. ACGME required numbers aren't the benchmark. They are the minimum. How well trained you are at the end of the day is the benchmark. Can you walk out of the program and practice surgery. Most chiefs that I know will say that residency feels too short sometimes because they realize how much they want to learn before they graduate and they enjoy how much they are learning by doing lots and lots of cases.
Personally, I'm a PGY-5. Since the start of May (3 days), I've done 13 cases. 2 CEA, 1 bypass, 1 EVARs, 3 lower ext angios, 5 dialysis accesses, 1 BKA. The first 4 cases are the 'major' cases that ACGME tracks, but I honestly got a ton out of the angios, access cases and the amputation because I did 80%+ of them without staff in the room. The 20% that they were around was intellectual, not technical. Decision checking, thought process verification, etc. You need sufficient volume that your staff feel comfortable with you doing these operations without them. You can't get that with minimal numbers and certainly can't get that without a ton of smaller cases in between the tracked ones.