I have a feeling you are overthinking the Matrix key system.
create account
create password you store somewhere safe
copy the key and store somewhere safe
when signing on a new device, copy-paste the key
Basically it’s just another password, just one you probably can’t remember.
Most of the client apps support verifying a new session by scanning a QR code or by comparing emoji. The UX of these could be better (I can never find the emoji option on Element, but it’s there…). So if you have your phone signed in, just verify the sessions with that. And it’s not like most people sign in on new devices all the time.