Healthy people are more productive, which mean they are better paid, which mean they have more money for healthcare, which means profits for the healthcare industry.
Finding cures is a good way of maximizing profits, the best way actually, and if the healthcare industry is not doing that, it means that something else is stopping them. It can be bureaucracy, it can be just because it is really hard, it can be some systemic problem linked to health insurance and government funding, but I don't see how the healthcare industry wouldn't want to cure people.
It is an industry where demand is guaranteed, diseases in general are not disappearing anytime soon, let alone aging.
yes and no. Finding treatments that require long term commitments is more profitable than finding cures. Look at the history of ulcer drugs. Pharmaceutical companies spent huge amounts to develop drugs that ameliorated symptoms, a two person team found a cure for most ulcers.