Any waiting period for calculation that won't annoy users is not long enough for an attacker to not still be able to spam, given that they will be solving them 2-100x faster with an optimized native implementation vs in a browser.
It also doesn't work as a turing test, because by their nature computers are good at batch solving proofs of work.
I once started an anonymous email service with browser-based PoW for antispam. It didn't work.
You'd need users to do like, several hours of in-browser PoW to make it viable as an anti-abuse measure. Anything less means a bot farm is posting spam dozens of times per hour.
Frictionless micropayments are still a pipe dream today, as any useful technology available to do so has basically been outlawed in the USA without a multimillion dollar license, and a KYC department, et c. It's a real shame because we have all of the technology for cash-based anti-abuse bonds and the like. It's just illegal to deploy it unless you go full MSB.