There’s nothing technically wrong with the strategy.

A few things to consider:

Spammers can also do PoW so it would slow them down but not stop them completely. Also, they could target specific accounts to focus the abuse. For example, all large accounts or only new users. 

A lot of people use their phones and PoW could have a deleterious effect on phone batteries. 🪫 

It might be better to have the PoW upfront so the “price” is larger but paid once to create the account rather than each time to send a message. Especially if there was a way to quickly blacklist their accounts everywhere. 

I’m still thinking about a WoT model where new users must be sponsored (followed) by an existing user. The nostr clients offer a few guided options on how to get “into the club”. 

Some ways of getting sponsored:

Attend a meetup / conference / real life and find an existing nostr user. 

Do a large PoW and send a DM to an existing user. 

Send a zap to an existing user. 

Etc.