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> 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?

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.

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.

Another example of legit usage of UDID: TestFlight.