There has been a lot of discussion about this topic lately.
I want to address a few questions.
By the time a new student has played 1 note I have started making mental notes about their playing. I have stopped hundreds before a scale was finished. When I do that it is always for a reason and I DO EXPLAIN why.
I give most of my students a warmup. The one I give them lets me check all aspects of playing in about 3 minutes. I can tell how much progress they are making that way.
I don't want to spend a great deal of time hearing warmups. I want to hear tone, phrasing, technique.... Boring YOU BET. It is a warm up not concert material. There is a REAL reason to warm up 1 playing aspect at a time.
I've stopped people in the first minute of a lesson to see what mouthpiece they are playing. This is usually because I hear a poor tone or cracked notes. I address it ASAP. There is no point in fighting faulty equipment. If it is wrong for you your teacher should tell you.
I have NEVER asked WHAT horn they are playing. Nor have I ever told anyone to buy a new one. I have played some students horns when asked. I have suggested valve work when needed.
My first lesson with Jake I played the first 3 lines of his warm up ONLY.
I had an open mind and I learned a great deal from that.