I think the main argument for the presence of US forces in EU is threat from Russia and the like.

Not every country would be happy about being showered with your radioactive fallout

Exactly why a bully country would meet resistance from many EU countries, due to creating the threat of nuclear fallout. Thus no US forces necessary?

EDIT: It's called 'nuclear parity':

https://www.armscontrol.ru/start/publications/dkp0731.htm

Obviously, Moscow was not satisfied with the situation that a total retaliatory strike, and hence unlimited nuclear war (equal to suicide), was the only response in the case of an escalating limited conflict. Thus, the USSR made titanic efforts and achieved relative nuclear parity with the USA in the early 1970s. The system of strategic nuclear weapons created a state of strategic balance in which each party possessed the capability to inflict unacceptable damage in a retaliatory strike – the essence of the concept of mutually assured destruction. At the same time, at this stage, neither party, theoretically, had the ability to gain superiority after exchanging counter-force strikes. However, the USA continued to seek such superiority. The most vivid example was the US forward deployment of nuclear forces in Europe and the Reagan doctrine of limited nuclear war.