Progeria is an extremely rare condition, 15 years ago almost nothing was known about it. Then Leslie Gordon and Scott Berns, both physicians, had a son who was diagnosed with it at 2 years old. They were able to find the cause, isolate the genes responsible, and adapt a drug to combat many of the more fatal symptoms. They had help, and luck. But they are doing the impossible.
Bonus: the drug may help slow aging in healthy humans as well.
Also: this has been mentioned on LW before, but without the awesome Do The Impossible narrative. I blame the BBC.
Yet no "rational" person would donate to a Progeria foundation because of the low incidence (1:8 million) , given that it falls under the "rare diseases in cute pup... err, children" category.
Let's count our black swans when they actually hatch... There are many ways to induce aging artificially and then fix it without affecting regular aging, just like there are many ways to cripple your mental performance and then ameliorate the damage without producing a useful nootropic.
(Besides that, progeria has been justified by its benefits in understanding serious issues which are compelling to a '"rational" person' - like everyone else's aging. Just google 'progeria "normal aging"'!)