It is not the controller's responsibility to know aircraft performance, nor the best route for the aircraft in question. The controller asked questions of the pilot that, in my opinion, should have gotten the pilot to think about their best course of action.
Aspen has some flight training, but really not that much single engine piston traffic. I fly within 10 miles of there regularly, but have never landed there due to the fees. And, at this time of year it gets a little busy with jet traffic on the weekends. I have listened in when the student pilots are trying to land, jets are coming in pretty rapidly and students get flustered with making 360's. The controllers seems to pick up on the students getting behind the airplane and give them vectors or otherwise try to simplify their work load. But, the controllers know which ones are the students because they took off from ASE.