You chose to take us down the path of cancer, not entirely unreasonable as I mentioned it. But it is clearly in the fringe extremes of my argument since it is one disease where, ostensibly, specialized care could really pay off. But it turns out that even in the case of cancer, the benefit of specialized care (for the most cancers at least) is small to zero.

If your local hospital can treat e.g. colorectal or breast cancer to the same degree as a specialized institution, then they can certainly competently treat the overwhelming majority of other issues that people show up to the hospital with, which are generally going to be substantially more mundane with rather more 'commoditized' treatment available.