> The purpose of a cancer hospital is to cure two-thirds of cancer patients... These are obviously false. The purpose of a cancer hospital is to cure as many patients as possible, but curing cancer is hard, so they only manage about two-thirds.

I don't see the contradiction here. The purpose of a cancer hospital is to cure as many patients as possible. "What it does" is cure as many patients as possible. The fact that as many patients as possible is currently (presumably) two-thirds is irrelevant. If major advancements in medicine or new types of cancer emerged which changed the percentage of people cured it wouldn't matter at all. "What it does" and "the purpose of the system" is still unchanged.