The other part missing with the “everyone will run their own relay” is that if you’re popular, even if you are the only writer on your relay you will end up needing a beefy infrastructure to support all the readers. Expecting every individual to be able to pull that off is a pipe dream. Much harder than running a bitcoin node.
Discussion
I can see running your own small relay for private family-and-friends networks. That would certainly work. But for a large-scale network looking to compete with the likes of Twitter you need serious hardware and bandwidth, and that's expensive.
Exactly. Personally I’m less worried about paid relays and more worried about who’s paying for the free ones (long term). The “if you’re not paying for the product, you are the product” adage.
What would you build if Twitter didn’t exist?