Many countries would ignore the patent and manufacture it, driving people to medical tourism, and then the patent will expire in 18-23 years anyway.

Patents run out and they are made public. If you go through the expensive process of developing a drug, you're likely to want to get a return on that. If there is enough evidence for the cure to work that a company wants to bury it, they're more likely to not patent it.

Also, this presupposes that the companies are actively trying to do evil. In reality, most people would rather have cancer cured than not cured. The profit motive can bend these incentives, but I think the caricature of a company full of amoral sociopaths making decisions to maximize human suffering are kind of... unrealistic.