According to this logic, Taiwan should keep the most advanced chips to itself, the EU should keep the most advanced chip lithography machines to itself, etc etc.

I mean, yeah they could. But what they get back for exporting is more than it is worth to them alone. Taiwan has no use for huge amounts of silicon and Europe has no use for SOTA lithography.

I don't see how that is the case with the US and leading edge AI. The US has a lot of use for that, and on balance, I cannot think of anything that is more valuable than super intelligent AI. It's basically the end game power for the human race.

Countries could try what essentially amounts to unilateral sanctions on the US to try and force sharing, but it's unlikely it would go well.

By the way, China will lock it's super smart AI in house too.

This isn't a new idea either, both the US and China have technology already that they keep to themselves.