Yes, they are guessable but your application should not rely solely on the "secrecy" of the ID to authorize access to a record. If you are worried about someone crawling your public API with wget or curl and an incrementing counter you should re-think whether your data are really public or not, or maybe rate-limit anonymous users, etc.
They also reveal something about the total number of records in your database, I guess that could matter in some contexts but it's never really been an issue in practice for me.
I have definitely used the technique of defining non-overlapping sequences in different shards (with Oracle, not Postgres, but they are very similar in this regard). It worked very well and was easy to reason about.
As a developer, the big issue I have with UUIDs is that they are impossible to read or type. You have to copy/paste and it isn't easy to look at two UUIDs and tell if they are different.
I use integers in general unless the specific use case demands something else.