At scale, yes. Because human males have significantly longer fertility periods than females, the specific adaptations of men who are healthier into later life can be passed onto offspring. The same applies to women who reach menopause while they're still healthy are able to continue caring for family without the risk of expanding the population, albeit for their offspring.

While human evolution is not predictive, it has selected for a wide variety of survival-associated adaptations beyond the mere individual.

>There only needs to not be a reason we need it to survive long enough to reproduce.

Humans had life expectancy even shorter than our fertility period until recently and they developed as social species hundreds of thousands years ago, for which living beyond fertility period is beneficial (grandparents were invented by evolution too).

> And bear in mind that most people don't have a problem surviving colds

That’s modern people with access to antibiotics etc.

> that was probably more true for much of our evolutionary history when we were living much more isolated lives, and not cohabiting with chickens and pigs

For much of our evolutionary history people were eating animals, getting viruses with them.

Or the risk of autoimmune disease?

If something clearly helps survival and not an improbable thing to develop, the chances are high we would already have it. But we don’t and most species don’t. It is not the default, there likely exists a reason why.

Inflammation is certainly not "free". It causes systemic damage.