[x]

There were people who voted for Reagan who thought that ending the Cold War would make it possible for America to scale back our commitments around the world.

That probably wasn't Reagan's own thinking, but I'm not sure that a post-Cold War expansion of our global obligations was something Reagan would have favored either.

[tcrlaf]

“That probably wasn’t Reagan’s own thinking”

No, it wasn’t.
It was the American Left’s idea, though. Remember how happy they were to spend the “Peace dividend!” once Clinton took office?