I’m the co-founder of Friendly Captcha [0], we offer a proof of work-based captcha since two years or so. Happy to answer any questions.
A big part of what makes our captcha successful in fighting abuse is that we scale the difficulty of the proof-of-work puzzle based on the user’s previous behavior and other signals (e.g. minus points if their IP address is a known datacenter IP).
The nice thing about a scaling PoW setup is that it’s not all-or-nothing unlike other captcha’s. Most captcha’s can be solved by “most” humans, but that means that there is still some subset of all humans that you are excluding. In our case if we do get it wrong and wrongly think the user is a bot, the user may have to solve a puzzle for a while, but after that they are accepted nonetheless.