Certainly for many applications, the autoint approach would be fine.

The benefit of uuid in this case is that it allows horizontally scalable app servers to construct PKs on their own without risk of collisions. In addition to just reducing database load by doing the ID generation on the app server (admittedly usually a minor benefit), this can be useful either to simplify insert queries that span multiple tables with FK relationships (potentially saving some round trips in the process) or in very niche situations where you have circular dependencies in non-nullable FKs (with the constraint deferred until the end of the transaction).