Anything non-k-sortable in a B[+,-]tree will cause a ton of page splits. This is a more noticeable performance impact in RDBMS with a clustered index (MySQL's InnoDB, MS SQL Server) [0], but it also impacts Postgres [1] in multiple [2] ways.

[0]: https://www.percona.com/blog/uuids-are-popular-but-bad-for-p...

[1]: https://www.cybertec-postgresql.com/en/unexpected-downsides-...

[2]: https://www.2ndquadrant.com/en/blog/on-the-impact-of-full-pa...