This is the idea behind hashcash[1], but instead of currency it's just a small proof of work. Some nominal PoW (a few seconds?) to bypass the spam filter smells like it would be remarkably effective at cutting down spam.
Nano currency (nano.org) makes this possible and has some working implementations.
takes microscopic amounts via Bitcoin's Lightning Network. Amazingly effective.
I've used this bot for microtransactions: https://twitter.com/lntxbot