I'm a bit confused as to what the use case for UUIDs are compare to incrementing integer IDs. I assume there are some big upsides (aside from the primary key issue which seems to have quite a few solutions at this point), but I'm just not aware of them.
As well as the other use cases mentioned, they're harder to guess than incrementing integer IDs so are a useful defense in depth to help stop people guessing URLs for resources.
This benefit can’t be understated: missing or buggy authorization checks are present in almost all real-world web apps and APIs I’ve encountered. A long random component (such as the 80 bits provided by ULIDs) covers up a lot of sins.
A ULID is 48 bits of timestamp plus 80 bits of entropy. These new formats just don’t have enough random-component entropy. 64 bits isn’t enough. Who cares in your millisecond timestamp wraps every 8900 years as they do in a ULID?