Those parasites that live in birds' nests and boxes? They'll have a go at you too. If you're at all allergic to bitey things, and you have many boxes to clear out, it's well worth wearing long rubber gloves to handle all the old nest material - it's often full of mites, fleas, flatflies etc etc.
I AM an ornithologist, I learned this the hard way! If you spend all summer monitoring nest boxes, bitten wrists and forearms become an occupational hazard. And, yes, Jeye's fluid, dilute bleach, hot water, any disinfectant, really, will help a lot to keep all those parasites in check.
Yes, in nature, tits' populations (and those of other obligate cavity-nesters) can be limited by the availability of natural holes. Our tendency to take down old trees reduces the availability, and various tree diseases (Dutch elm disease, sudden oak death, ash dieback etc etc) aren't helping either. If it's a choice between having a hole that's full of mites and no chance to breed at all, you'll take the mitey hole. But if the nestboxes are openable and cleanable, why not open 'em and clean 'em? The tits should be able to hatch of more broods, bigger broods and healthier ones if they're not having to feed their chicks' parasites as well as the chicks themselves.