Don’t email spammers just spoof the domain or send without a domain?
They do both, depending on the spammer and the type of spam they send. In e-mail, you have an e-mail server, you can use it to send mail to users on other e-mail servers. Each e-mail server can choose to accept or reject email from other e-mail servers based on whatever reason they want. AP/Lemmy/Mastodon is basically identical to this. I'm not sure how exactly bluesky is setup but I get the impression it's similar. In Nostr, servers aren't federated (each relay is seperate, if you want to send/recieve content to another user on a different relays you just talk to that relay directly instead of having "your relay" act as an intermediary), but the structure is still pretty similar.
Nostr does have this hashcash type system (requiring proof-of-work to weed out spam), but I haven't come across any relays that actually enforce it, it will be interesting to see if that changes in time. I also saw a GitHub issue about adding something similar to AP but I think they chose not to implement it.