The OP reports individual donors contributing in excess of $100 million to particular causes. We've spoken often here about the various inefficiencies in the current research structures: top scientists spending too much time writing grants; disincentives for the curiosity-driven research that often leads to breakthroughs, etc.
So the question: is investment on the order of $100M+ sufficient to set up a private research facility with research "done right"? (By which I mean, of course, the way I would do it. :) ) It's easy to imagine a private facility that recruits top-notch but frustrated scientists from various schools, sets some important problems for them, and sets them free from grant writing, publishing pressures, etc.
The obvious objection is that the donor would call the shots and subvert the research... but on the other hand these sorts of donors are already willing to just fund research with no personal input into process.