Several solutions exist. We have Proof of Work for notes and paid relays. If I set my client to only show notes with a minimum Proof of Work of 1, they all go away, and so does nearly all of the comments from regular people, because most people don't use PoW. Paid relays are the simple and easy fix. I set my feed to not show content from public relays and all of the noise disappears. However, not everyone uses paid relays.

As for your suggestion, pay per note is a concept that relays can implement. The payments go to the relay operator.