Perhaps immune-based therapies like CAR-T are based on the premise that there are many cancerous cells in your body all the time, but your immune system deals with them, and it’s only when it fails to do so that you end up in the pathological state. So the “single cure” is the normally-functioning immune system?

That might be part of it. And yet sometimes people with normally-functioning immune systems also get cancer. So while that might be an effective treatment for some patients it's not going to be a universal cure.