> Proof-of-work is what allows you to successfully combat bots, spam, and trolls, as it brings real cost to destructive actions 

Spammers are willing to spend money to spam.
They go as far as buying lists of email addresses, they'd have no issue running POW algorithms if they need to.

If anything spammers may be more willing to pay than the average social media user.
Paywalls don't protect you from spammers. See spammers on Twitter with the "verified" badge.