There's this paper from 2004: "Proof-of-Work Proves Not to Work": https://www.cl.cam.ac.uk/~rnc1/proofwork.pdf

The conclusion back then was that it's impossible to make a threshold that is both low enough and high enough.

You need some other mechanism that can distinguish bad traffic from good (even if imperfectly), and then adjust the threshold based on it. See, for instance, "Proof of Work can Work": https://sites.cs.ucsb.edu/~rich/class/cs293b-cloud/papers/lu...