EUV was developed with in a Cooperative Research and Development Agreement between the US Department of Energy, Intel, ASML, and so on - giving Congress control over who ASML sells the EUV technology to.
So yes, US companies do have a choice. They can lobby Congress to cut off TSMC from their main hardware and parts supplier entirely, crippling it altogether, except for their Arizona plant which is ripe for nationalization for natsec.
TSMC certainly brings a lot to the table but if they were completely knocked out, it would just deprive the world of the top end of fab capacity for a while. On the other hand almost every fab in the world depends on ASML for parts and maintenance, even the old fabs on legacy nodes.
Taiwan is too dependent on the USA ATM to make that choice. If they were to go it without the USA, the only choice would be to become an actual bonafide province of China, they aren't going to exist on their own. Almost everyone else outside of eastern Asia, however, can make a different choice.
So yes, US companies do have a choice. They can lobby Congress to cut off TSMC from their main hardware and parts supplier entirely, crippling it altogether, except for their Arizona plant which is ripe for nationalization for natsec.