I don't think there is any PoW that results in acceptable performance for the user (especially on mobile) while also making the cost for an attacker high enough to deter them.
Even renting the compute on AWS, it only costs $0.01 per minute for the equivalent of a decent desktop computer (c8g.4xlarge). While an attacker will likely either use a botnet, or hardware better suited for solving the PoW than the hardware the user is using.
Though CAPTCHAs don't really work well anymore either, since solving services are quite cheap. Recaptcha is nowadays primarily based on other factors, like IP reputation, susceptibility to google tracking, and behavioral scoring.
Even renting the compute on AWS, it only costs $0.01 per minute for the equivalent of a decent desktop computer (c8g.4xlarge). While an attacker will likely either use a botnet, or hardware better suited for solving the PoW than the hardware the user is using.
Though CAPTCHAs don't really work well anymore either, since solving services are quite cheap. Recaptcha is nowadays primarily based on other factors, like IP reputation, susceptibility to google tracking, and behavioral scoring.