If you want a simpler example that doesn't involve biotech research, I would just look at the diversity of animal welfare organizations, and their relative quality. Some of the best animal welfare organizations in terms of impact are local rescues run by (in my experience) spouses of wealthy career-people (executives, lawyers, etc.) who have a ton of free time and love animals. But then there are also plenty of animal welfare organizations with questionable motives, and questionable spending patterns (fraud, embezzlement, etc.).
If a big public charity is able to cure a cancer type (eg. lung cancer), then it's next aim would be to try cure another cancer type. Let's just say they are somehow able to cure all the cancers, and therefore they cured cancer, then there's distribution of the cure, with a focus on 1st world but then it would have to go to developing nations too. Along the way, there may be issues that arise in recovery from the cure, so money towards helping survivors there. Shift goal, shift goal, shift distribution/priority of donations, on and on and on. For the proper charities that do want to meet their goals, something like this is what they'd do.
If you can find and patent a cure to cancer, you can charge whatever you want for it, at least in the US. I don’t think profit would be an issue.
And even if ending chemotherapy would discourage the incumbents, smaller companies would love the opportunity to kill them.
For example, Polaroid didn’t want to embrace digital cameras since they made tons of money selling physical film. But all the smaller camera companies didn’t care, since they weren’t benefiting from that and wanted to just take Polaroid’s market share. And that’s why digital cameras took off regardless.
I mean, yes, "I haven't looked into the specifics, but working from the first principles I came up with in 3 seconds, cancer research charities are in fact cancer on society" does come off a bit reductively cynical.