Having shame would require the LLMs to actually be able to recognize mistakes they make.

People love to put a lot of meaning on what an LLM responds with when asked why it made a mistake, but it's critical to remember that the answer to that prompt is just another series of probabilistic tokens, and has no actual relation to how the error happened.

They "recognize" mistakes just fine because you explicitly tell them. They recognize them well enough to correct (...sometimes). The way in which mistakes don't register is "Oh shit, that bad result was a result of my inappropriate actions. I must pay attention to not doing that again or the user will think I'm an idiot. I should even think about it some more to avoid the whole class of mistakes". Think of emotions as an attention mechanism that LLMs lack.