> Another way (which I'm quite partial to) to separate wheat from chaff is to use identities that cost a few dollars.

Spammers pay when they need to.
I suspect they might be more willing to pay than regular users, not less.

Spammers buy bulks of email addresses, or spend money on other shady shit. They pay to spam.
The willingness of someone to pay isn't an indication of legitimacy.

But the pay-to-register, rather than pay-to-post, just might work (since you can block bots manually at that point). PoW, however, would be the only way to verify such payments.
Otherwise I'd have to trust relays to perform verification. If I trusted relays I wouldn't need Nostr.