Earlier quoted context omitted.
> The current main incentive against cheating is that miners will lose their invested PoW (compute time + electricity) if they cheat and get their block thrown out. However, with a useful PoW, this calculus changes. Now, the PoW is no longer "wasted" when the miner cheats and gets caught as the PoW is now useful for something besides mining. So you spend $x on (compute time + electricity) to mine a useful PoW worth $…
$y + $z must be greater than $x. If $y is money and $z is scientific contributions... $y is most likely not something people are offering money for. So in an open market its value is at or near $0. So $z by itself must exceed $x. To not care about the $z, $y must exceed $x by itself and that seems really unlikely for the types of things that OP suggested instead of proof-of-work.
Edit: silly question on my part. y and z should be trivially interchangeable. Your argument appears to rest on the idea that the monetizeable scientific worth of the work would dominate the worth of the crypto token itself, since there would be limited value in an already-mined result beyond standard blockchain speculation - is that the case?