For the moment, US companies do actually care what the UK courts and regulatory bodies say, because the trifecta of US-UK-EU is what tends to form a base of what the rest of the world decides. It's why Microsoft have been so unhappy about the UK's Competition and Markets Authority initially blocking the merger with Blizzard: even with the US and EU antitrust bodies agreeing to it, it did actually matter if the UK didn't agree (I am so disappointed in the CMA finally capitulating). And some of the lawsuits against the AI companies are taking place in the UK courts, with no indications that the AI companies are refusing to engage. Obviously at this point it's hard to say what the outcome will be, but the UK legal system does actually have enough clout globally that it won't be a meaningless result.