I personally wouldn't like to put caching in Postgres, even though it would work at lower scales. But at that scale I don't really need caching anyway. Having the ephemeral data in a different system is more appealing to me as well.

The caching abstractions your frameworks have are also likely designed with something like Redis in mind and work with it out of the box. And often you can just start with an in-memory cache and add Redis later, if you need it.