Of course it’s not technically “free”, but if it only needs to compete with mobile devices (even hundreds or thousands) it’s practically free.

A modern MacBook Air is 1.6 million times faster at sha256 than an iPhone is (citation needed, this is GPT knowledge). The gap is so massive

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But you are always supposing users would be constraint to mobile CPU, and that's not entirely true:

NIP-13 allows for Delegated Proof of Work:

https://nips.nostr.com/13#delegated-proof-of-work

We all can play the same game of spammers 😉