Weak parts of medicine
@Ben: Not a lawyer, but my understanding is that hospitals fall into a separate category, which is exempt from that restriction but has even more onerous other restrictions:
https://www.healthlawyers.org/hlresources/Health%20Law%20Wiki/Corporate%20Practice%20of%20Medicine.aspx
https://en.wikipedia.org/wiki/Certificate_of_need
Hmmmm interesting...
"Although venture capitalists own a piece of One Medical, Lee says that he's compliant with the Corporate Practice of Medicine Statutes which prohibits non-physicians from having ownership in physician practices or employ physicians. Collins says that PPMs exploited a loophole which allowed for small stock ownership without breaking the rules." - https://www.forbes.com/sites/zinamoukheiber/2011/09/07/can-one-medical-group-succeed-as-a-new-model-for-physician-practice-management/#1ee00d8d4888
@Alexandra: There certainly is a market there, but then the big issue is how to compete effectively against scams / placebos. An average person who is seriously ill, doesn't trust the medical establishment, and is willing to spend large amount of cash on experimental treatments probably won't have the knowledge to read through statistical analyses or biochemical pathway diagrams. If treatments succeed or fail in the market based on what individuals each choose to buy, and individuals choose what to buy based on their default instincts / what sounds right to them, it's possible to design pretend treatments that are much more convincing-seeming at first glance than real treatments. Treatments that purport to "cleanse" the body of "toxins", for example, are very popular, playing to people's naturalism/purity-vs-contamination heuristics (which do have some grounding, but almost everything sold in that category has little or no effect). Dietary treatments for non-diet-related conditions are another big one, as are treatments based on "energies" or over supernatural forces. In essence, if tomorrow you invented the cure for cancer, but it wasn't covered by insurance or FDA-approved, you'd not only have to find cancer patients willing to buy it, you'd also have to make sure those patients didn't first spend all their money on all of the fake cures for cancer (Wikipedia has a convenient list, https://en.wikipedia.org/wiki/List_of_unproven_and_disproven_cancer_treatments). Not saying this is impossible or anything, but it's a major problem to confront.