What Good Are US Troops In Europe?

The US has some 66,000 troops in Europe with another 1.5 million EU troops from various EU countries.

It is generally assumed that there would be no military response by Europe -- even if Putin invaded the Ukraine.  I can understand that no one wants war, but what good are the troops if their use is ruled-out in response to even non-EU military aggression??  Russian troops only number about 770,000 (with many more reservists).

For that matter, why are there 50,000 troops in Japan?   For what possible deterrence?  And at what cost?