That's an interesting idea. It's effectively an attempt to create a distinction between legitimate identities and potential spammers by adding a "cost" to creating an identity, yet without the need for a centralized authority.
However, I don't know how effective it would be. The PoW would have to be high enough that it imposes a significant cost for spammers to have to spin up a new identity once the one they were using is no longer being seen by most users. Yet, that also means it will be a considerable wait for a new user on standard hardware to generate enough PoW to finally be able to post.
Indeed, a spammer could have his GPU working overnight to have multiple Nostr keys ready to go, so that as one is detected as a spammer, he just uses the next one in line, with the PoW note already having been generated.
I think the cost to the new user would be greater than the imposition caused to a determined spammer. Indeed, the more I look at PoW as a possible spam deterrent, the less it makes sense and really just ends up being a deterrent against new users in general. For it to be effective at deterring spam, it needs to be a high enough amount of PoW that it is an annoyance to average users, too. Especially those posting from mobile devices.