I wonder if some rich people could start a form of charity where they just pay a few incredibly brilliant people a good salary to go do whatever research they want for the rest of their lives. Sort of like patronage. Just bypass the whole grant funding cycle and work on whatever you want, because you're a genius and want to study things other people don't like or understand.
Another issue with relying on charity is that there is often strings attached to the money donated. We really want to allow students, scientists, engineers, etc. to have agency, not be under some wealthy person's patronage.
A first problem is how to recognize these incredibly brilliant people. The current answer to this is the tournament to tenured professorship. If you select those who already succeed in this system, you are not really doing anything new, so something different should be done but it is not clear what.
A second difficulty is the "rest of their lives" part. It's quite hard to believe ROI would not be required when rich people are involved in some way or other. Charity is PR, and so the system will optimize for PR.
It's kind of like what happens with the people who invest in startups... the founders who fit the investors' conceptions of what brilliant people look like get funded. It's also a big problem in philanthropy and why many times it's better to have (even slow and inefficient) government depts with set criteria and review processes deciding who gets funding.
Something like this happens, actually. It's often in the clothing of small nonprofits with small teams of people who are brilliant, or who are basically the support department of the 1 or 2 funded geniuses. Question mark on the efficacy.