WoJ states that wizard-longevity is a function of them doing magic. The more magic they do, and the more powerful it is, the longer they live. Charity won't have any extended lifespan, because she stopped and let her magic wither away.
Butters theorizes (and there seems to be pretty decent evidence for the argument) that the main physical benefit to the WK-mantle -- the strength & speed &c -- is just to take off all the inbuilt "governors" and "safeties" that let an organism live long-term, letting the WK act full-time as if they were on an massive adrenaline-spike, without regard to pain or injury.
Wizard healing is, I think, a related thing to wizard longevity.
What if the main magical benefit is a similar "governor off" effect, letting the WK (if a wizard) do more & stronger magic... leading to a boost in the longevity AND the healing?