The idea of colocating data and behavior is really a quantifiable reduction in complexity. It removes latency and bandwidth concerns, which means both operational concerns and development concerns (famously the impact of the N+1 problem is greatly reduced). You can absolutely argue that networked Postgres is better for other reasons (and you may be right) but SQLite is about as boring and predictable as you can get, with known strong advantages. This is the reason it’s getting popular on the server.
That said, I don’t like the idea of creating many small databases very much - as they suggest with Durable Objects. That gives noSQL nightmares - breaking all kinds of important invariants of relational dbs. I think it’s much preferable to use SQLite as a monolithic database like it’s done in their D1 product.