"But the professors say their bigger gripe is with the procedural, rules-based approach in all of Mr. Khan’s videos."
Well, that's how they teach it in public school, here are the steps, no explanation of why it works, just accept that it works and memorize the steps. So if you want to attack teaching the procedure instead of the concept, look at just about every math teacher in K-12 first.
Your problem here is that you are using your own experiences and extrapolating to the general. You think any math teacher you see teaches like that. This is not the case. The teachers that have been the loudest critics of Khan tend to be really excellent teachers. You know why? Teachers who teach like you describe don't care enough about their teaching let alone worry about what some website is doing.