> If a device provides this feature and it does not contain any other secret information introduced in it by the manufacturer, then it allows the owner to have any kind of backup that is desired.

Precisely. The Ledger Nano S (and probably the Nano X too) allows to do exactly what you describe, the very way you describe it (three wrong PINs, on purpose or not, and the device resets itself to factory default and, as you wrote, at that point it's unusable until you enter again a master secret (either your old one or a new one: the device has no way to know and doesn't care).