I'd expect the opposite: higher fitness -> immune system more busy with repairing wear&tear. Lower fitness -> immune system bored and more reactive to any suspicious cellular activity.
The repair of the wear and tear seems to provide more opportunities for the body to reject cancers. Also, aerobic activity may encourage selection for oxidative metabolism which is very suppressed in most cancers. It's counterintuitive but the epidemiology is very clear that exercise is protective. It doesn't wear you out faster but rather helps you rebuild and maintain yourself more rapidly (without which, you wear out).
That might be true in the extreme ends, say for Ironman athletes, but a bit misleading as a summary since we already have lots of data that moderate exercise correllates with reduced risks of everything from getting a cold to heart disease. If we’re comparing to people who don’t exercise, the alternative should be moderate exercise, not high intensity training. Also a bored and over-reactive immune system can be a pretty bad thing.
When it comes to dealing with any biological systems always look for outcomes over mechanisms. There is plenty of evidence showing exercise improves almost all markets of health
What's the mechanism behind that? Being "more fit" is not exactly one single thing.
is it obvious that good fitness is related to good immune function?
It seems obvious when you see your own body aging and slowly loose both.