No, because phones that lock keys in hardware effectively prevent that, and that works only with hardware that prevents its owners from having full control an doing what they want with their hardware.
"Unextractable keys" works with hardware that you don't "truly own".
What if you truly want the security properties provided by a device which can keep keys in a way where you fully control their use but its extremely hard for anyone to extract them?
However if you can get so far as to get the secret from the TOTP app, you can as well back up the entire phone and restore elsewhere, can't you?