AMRAP workouts are almost never executed "until exhaustion" - they are usually time-limited. There are other types of workouts which have increasing loads or repetitions until the athlete can't keep up - usually called "death by" (yes, it has "death" in the name, surely that means Crossfit is a death cult) - but those not exactly "until exhaustion" - at least not always, since if you can't lift the next weight in the line it doesn't mean you necessarily exhausted (though it may be). I don't see why this would be more prone to injury though - most workouts are meant to make you tired, and when you're tired, you may lose form, and when you lose form, you may be susceptible to injury, especially if you let your ego run away from you. That's where coach comes in and tells you to stop doing stupid, drop the weight and fix the form, or change the exercise.

Yea, usually motivation by your peers is a good thing but in CrossFit, it’s detrimental as it forces you to stop listening to your own body because of peer pressure.

that's true of any exercise that involves a group