By this logic the Chinese should have just given up and let the American AI companies have the market because they were so far behind. I'm sure Europe has the capability to distill other people's frontier models to catch up if they wish to do so.
There definitely have been Chinese companies with models that fell behind, which is the more direct comparison.
As for the EU in general, there are not a lot of known options. There are some working on things.
The US, the EU, and China all have frontier labs that have yet to release anything.
What’s the mechanism that could today prevent other companies from using LLM outputs to train their models?
Mind sharing such cases? I'm not aware of any so far. There's the one with images, but that's commonly miss-understood, that case was ruled on a technicality (i.e. copyright needs to be attributed to a person, not a model)
That is not the direction American judges are taking. Right now, they are saying that LLM output cannot be copyrighted. And if looting copyrighted works for training is fair game, I really don’t see how one could argue that learning from other LLMs is not.