Could Generative AI Improve Compilers?

With the growing popularity of generative AI I have thought what real world topics could it address (I know art is important but I mean engineering uses). What would be the outcome if we could train a model to generate compilers for new or existing syntaxes. I have not pursued this idea but thought it might be an interesting conversation to be had.

The main issue I can imagine is there is a relatively small training data set that could be used. Also, we see that tools like ChatGPT struggle with understanding (tackling physics problems etc).

Wondering what peoples thoughts are about this or if its a stupid idea.