Also entire classes of bugs. You screwed up a JOIN, or an application-level lookup for that matter? With UUIDs you'll get no results, with sequential ints you'll get a valid but wrong result.
Or worse, the right result for the wrong reason. I've actually seen a case where creating a new entity in the application populated X records in X child tables, each with a sequential ID, and as a result all of them had the same surrogate PK. They were 1:N relationships in principle, but the software wasn't feature complete yet so the actual records were all 1:1.
Years later one of those tables finally received some extra records, and it caused a really weird bug because a query had accidentally used the PK instead of the FK as a join key, but for years it had happily chugged along because the two columns were in sync.