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Proof of burn is more efficient and harder to game. Emails are already being send from botnets, which are already used for mining.

Spam will exist as long as it is profitable. If inboxes only show email which has paid a very small cost (like .001 cents), it would quickly make spam unaffordable.

> Anecdotal reports place the retail price of spam delivery at a bit under $80 per million [22]. This cost is an order of magnitude less than what legitimate commercial mailers charge, but is still a significant overhead; sending 350M e-mails would cost more than $25,000. Indeed, given the net revenues we estimate, retail spam delivery would only make sense if it were 20 times cheaper still.

https://www.zdnet.com/article/how-email-spammers-really-make...