Earlier quoted context omitted.
The problem is, that it still requires an address (be it tor or IP). Even if you run the script locally, there is still a need to communicate input and output. So people can just ddos that page. Works great for combating human spam though. You tend to behave better if your login took half a day to get and expires quickly when not used. Plus build in cool down time after getting banned.
Behaving better isn't the only outcome. Another outcome is leaving the service permanently.
The merits of proof of work should be discussed for the specific scenario. If it allows for reputationless discussions and throwaway accounts, how high is the cost really? In comparison to banevasion problems, moderation overhead and the resulting attack surface requiring more resources while deteriorating the channel? Otherwise impact less emergency breaks for idiots might be reasonable solution. Its not much different from timed bans.