The check has to apply to people and bot visitors the same. If you're expecting a blockchain registered spend before the content is visible, basically nobody will visit your website.
I don’t think OP meant you pay directly, just that you volunteer to do some part of the PoW (of some chain designed for this purpose) on behalf of the site, to its credit.
That’s not much of a different ask from Anubis. It just commandeers the compute for some useful purpose.
I don’t necessarily mean “useful” in the sense of scientific research or something. Simply transferring value to the creators of the resource being accessed (a la a blockchain) instead of doing throwaway work would be an improvement.
It would be more like using a javascript webminer to mine for you a bit before you get access. This would be the "proof-of-work" needed to then proceed to scrape.