Suppose you have a newsletter with 10,000 subscribers. You need to perform a proof-of-work the first time you send an email to each new subscriber; so, 10,000 proofs-of-work. Each proof-of-work costs $0.001. This adds up to a grand total of ten dollars.

Or, to put it a different way: $0.001 is very roughly equivalent to a few minutes of CPU time. So if you have a single-core server dedicated to running your mailing list, you can onboard several hundred new subscribers every day.

Remember, the sender only needs to pay the proof-of-work when someone first joins the mailing list and receives the initial message. So, I don't see how this will kill mailing lists at all.