> namely tying together information from multiple applications

That is not a legitimate reason. If I want my applications tied together I'll manage that myself.

If you have a suite of apps (free/paid) or that work together in a meaningful way, you can use a unique pasteboard to persist shared information.

If you did that for advertising reasons, I'm sure Apple would reject/revoke the apps once they found out about it.

Would that persist across resets?

The pasteboards are persistent across power-cycling.

They may even survive restoring from backup (say after upgrading iOS or moving to another device), but I haven't tested that.

If you mean reboots, then the various applications in the suite could store the identifier on disk and recover it if it is missing; and, if you mean restores, that place on disk could be something that is backed up by iTunes.

Another example of legit usage of UDID: TestFlight.