I think you're mostly right, but it depends - and presumably Eastern Europe would want us there too in the event of a Russian invasion.
The problem when they "want you" is that your occupying Army now has to do things like government administration and nominal policing, something the United States military hasn't done, at least convincingly well, since WWII (one could make an argument this started going well at the end of the Iraq war but I would heartily disagree). It's just a different type of occupation.
It would be "maintain forward bases during a dynamic conflict with or without the support of the local government", not "try to turn Afghanistan into an 18th century state for the first time, or fix Iraq".
The problem when they "want you" is that your occupying Army now has to do things like government administration and nominal policing, something the United States military hasn't done, at least convincingly well, since WWII (one could make an argument this started going well at the end of the Iraq war but I would heartily disagree). It's just a different type of occupation.