> If you have a primary key whose generation is truly random such that each number is equally likely, then that b-tree is always going to be balanced.

Balanced and uniformly scattered. A random index means fetching a random page for every item. Fine if your access patterns are truly random, but that's rarely the case.

> Why are you clustering on a random opaque key?

InnoDB clusters by the PK if there is one, and that can't be changed (if you don't have a PK, you have some options, but let's assume you have one). MSSQL behaves similarly, but you can override it. If your PK is random, your clustering will be too. In Postgres, you'll just get fragmented indexes, which isn't quite as bad, but still slows down vacuum. Whether that actually becomes a problem is also going to depend on access patterns.

One shouldn't immediately freak out over having a random PK, but should definitely at least be aware of the potential degradation they might cause.