What if we brought back conscription? For science, not war.

So, required graduate school for everyone, and make sure they have money for it? Why not just sponsor two years of graduate school for certain fields of study? Which is close to what we have now, only it's voluntary.

How does one tell if a conscripted researcher is slacking off on the job, or if the job isn't just impossible?

Who is going to pay for the vacuum chamber and other hardware for researching the Casimir effect? Hardware like Anton which D. E. Shaw Research uses for protein folding? And how much training does one need even to start researching supersymmetry? That's at least a couple of years into a PhD program already, so only a select few could do it, and only those that were interested in it in the first place.

"a hard problem that has the potential to dramatically aide human beings" ... and who decides? Why are massage training, and singing, and a push for a 35 hours work week less important than cold fusion?

In other words, it sounds impractical, inefficient, and fraught with political difficulties.