The "collapse" you're talking about is a reduction in the diversity of the output, which is exactly what we should expect when we impart a bias toward obviously correct answers, and away from obviously incorrect answers.

Further, that criticism is based on closed-loop feedback, where the LLM is training itself only on it's own outputs.

I'm talking about open-loop, where it is also evaluating the responses from the other party.

Further, the studies whence such criticism comes are based primarily on image generation AIs, not LLMs. Image generation is highly subjective; there is no definitively "right" or "wrong" output, just whether it appeals to the specific observer. An image generator would need to tailor itself to that specific observer.

LLM sessions deal with far more objective content.

A functional definition of insanity is doing the same thing over and over and expecting different results. The inability to consider it's previous interactions denies it the ability to learn from it's previous behavior. The idea that AIs must not be allowed to train on their own data is functionally insane.