Supporting multiple devices is a hard problem. We worked for a long time to enable it. Not Bitcoin protocol specific, but some words about our asymmetric key based multi-device solution here; https://www.mepin.com/lost-device/
The solution ^ still require a traditional account registration, or at least connection to the device that was used to create the account (if we go with passwordless registration). Otherwise, "must link their MePIN app to an actual user account in the target service" wouldn't be true.
