In my experience, the primary benefit of getting good at improvisational performance to delivering prepared content is that I can handle unexpected events.

If I get heckled, or challenged, or I go up on my lines, or my scene partner does something completely unexpected, or a prop turns out to be missing, or the couch suddenly collapses, I can ad-lib some kind of a plausible response and maintain an air of everything being under control.

And simply knowing that helps reduce performance anxiety, so it pays off even in the more common case where nothing goes catastrophically wrong.