Well you're not using "Bitcoin" per se, it's just adding proof of work to messages. Coracle does this. It just uses your computer to do proof of work on a hash of your message.
No reason why it couldn't work for public notes too. Nothing is encrypted.
It's the same kind of thing that Anubis does: Force the user instead of some "captcha" to do a small amount of computational work, that's no problem if it's a human but becomes uneconomical if it's a massive web scraper" https://anubis.techaro.lol/