If, as I suspect, interesting-ness is uncorrelated to potential benefits, we should still ensure that interesting projects are funded.

This is not the correct conclusion of your argument. You are entitled to: "We should not fund uninteresting projects."

If I tend to find useless math problems interesting and useful ones tedious, I can stop doing math and try to find another field (among many alternatives). If I am considering a funding proposal for a problem which is predictably useless, I can simply not award funding.