I mean in my opinion GPL licensed code should just infect models forcing them to follow the license.

You can do this a lot by saying things like: complete the code "<snippet from gpl licensed code>".

And if now the models are GPL licensed the problem of relicensing is gone since the code produced by these models should in theory be also GPL licensed.

Unfortunately, there is a dumb clause that computer generated code cannot be copyrighted or licensed to begin with.

> Unfortunately, there is a dumb clause that computer generated code cannot be copyrighted or licensed to begin with.

Can you point to the clause? I have never seen it in any GPL license.