Why would keeping cull animals make them any more hardy
I actually do agree with you that certain animals must be culled because they are prone to failure in one or many ways, and should not breed. No disagreement there, the only thing I'm speaking against is the arbitrary culling of an animal for a problem it can overcome which may not be something it is likely to come down with again, hence the need for proper diagnosis as to whether or not it's an inherited problem or particularly weakly animal. I've got no argument against you or anyone being part of the natural selection process, as you said, in fact I believe that's a necessary part of every responsible farmer's job. Within reason and there's exceptions to every rule...
Animals will get ill when exposed to something they do not have resistance to, so culling them for that won't engender resistant genetics. For example: if you've got an endemic disease on the farm and your stock are resistant, but a certain animal comes down with it twice, that'd be a culler, but if you don't have that disease and it gets introduced to your herd and your animals come down with it, that's in need of treatment, rather than culling. It's more about finding whether or not it's the animal's 'fault' in each case. Or it is anyway in my opinion, everyone's entitled to theirs.
I wouldn't cull for mastitis unless I knew it was a congenital problem or the animal was otherwise nonviable, for instance too damaged. I would prefer to know for sure, so I could remove the family line if necessary, rather than keep culling the symptom, so to speak, and never finding the cause of disease. I don't tolerate problem makers either, I cull for less than hardy reactions to disease or injury, but in order to achieve strong stock I give animals a chance to heal from any assault they seem inclined to. If their immune system can't buck up and do its job with a little natural support, I cull; I wouldn't go so far as to use antibiotics except maybe for a pet under extenuating circumstances.
Over each generation of them being allowed a chance to dominate the disease with often only garlic as support, I've obtained measurably tougher and tougher stock, breeding even tougher stock in turn, and now problems that were common, aren't; in fact most are gone completely. That's what I meant regarding the hardy breeds we've inherited, compared to the more modern breeds which can't cope in the same environments their ancestors were reared by our ancestors within. The only support they received was natural and if they couldn't make it on that they died one way or another, but they were often given more chance than their modern descendants. That's where the hardy comes into it, it's a toughened immune system and better adapted DNA due to being 'in the wars' and emerging victorious. If that ewe's mastitis wasn't her fault, and she survives and emerges tougher, then is culled anyway, that strengthened immune response is not passed on to any offspring, which I would consider a loss. If she's predisposed for some reason, better to know for sure and inspect her family line too. But all this my be irrelevant to someone who isn't working on their own breeds, I don't know your situations, so maybe what you're doing is more relevant to your situation.