> Where you e.g. cannot coordinate the creation of your primary keys.

You are writing your data into a DBMS. Coordinating the creation of primary keys is one of the cheapest tasks around, if you can't do that, how is your database still online?

> Or where you cannot allow them to be predictable.

You don't need to export your PKs for the rest of the world. You can have non-predictable data outside of your PK. Yes, a different column will still have some of the problems with index maintenance, but it becomes a much smaller problem if only one table cares about the value.