Actually, a cyst meets your definition of unregulated cell growth. It's just slower / less greedy. The distinction between a benign tumor and a malignant one is generally ascertained by the process of "let's watch it and see what it does", so I'm not convinced that "cancer" is defined more usefully than "illness".
In my opinion, and my medically-educated mother's opinion (really, I get it from her), people don't look for "a cure for cancer" because they think they can make progress from that viewpoint. They do it because they're looking for funding.
edit:
You might compare "died of cancer" to "died of old age". Old age used to be an accepted cause of death. When autopsies started happening, it was quickly noticed that people who had died of "old age" always had some other, more immediate cause of death. But it turns out that if you take an old person and do your utmost to prevent / cure / treat all of those more proximate causes, eventually one will get past you and they will die.
In my opinion, and my medically-educated mother's opinion (really, I get it from her), people don't look for "a cure for cancer" because they think they can make progress from that viewpoint. They do it because they're looking for funding.
edit:
You might compare "died of cancer" to "died of old age". Old age used to be an accepted cause of death. When autopsies started happening, it was quickly noticed that people who had died of "old age" always had some other, more immediate cause of death. But it turns out that if you take an old person and do your utmost to prevent / cure / treat all of those more proximate causes, eventually one will get past you and they will die.