If your error logging is leaking privileged information to attackers that's a completely different problem from what you should do in code when throwing exceptions.

Wrapping exceptions to remove information is mostly a pointless exercise. You should be doing it only to add additional context.

It's not a different problem, my whole point was that letting exceptions bubble is not a universally acceptable policy. Sometimes you want to bubble, sometimes you want to wrap, and sometimes you want to wrap with information hiding to avoid leaking information.