One place we're avoiding ULIDs (and other counters) is in publicly-facing IDs. Preferring random to help keep them unguessable. (say what you will about security-through-obscurity).
So we do ULIDs for private IDs. Random UUIDs for public IDs. Seems to work well.
You don't have such issues with randomly generated ids, unless someone obtains a full dump of your database (in which case you will have to think about bigger problems anyway).
And the reason for that was to have lexicographically sortable IDs (even if not monotonic, which would require an extra server) so we didn’t have to index a timestamp column for chronological ordering. The alternative was to have a traditional integer sequence but it’s not always ideal to expose those on your API.
That also applied to our test suite so the choice was to use KSUID but still index a timestamp for accuracy, or just use an alternative with more precision.
Native DB support is irrelevant to me for randomized bits unless it affects storage, sorting, paging, etc. Does it?
You can also write a plpgsql function to generate these ULIDs in the database.
I ran into this last year - storing them as UUIDs works great, unless all of the drivers for the language you're using (Go, in my case) try to cast/validate those bytes as a UUID before you can access them.
Is there some value to UUIDs over ULIDs that make these discussions largely revolve around Autoincrement vs UUIDs rather than Autoincrement vs ULIDs(and friends)?
[1]: Again, totally out of my wheel house.
edit: Apparently UUIDv7 exists, which is similar to ULID, so my question pertains to UUIDv5 and below, i think.