TOTP as a "something you have" approach to 2FA is entirely dependent on how well the device secures the secrets.
An RSA key's private key is (nearly?) impossible to retrieve. The Google Authenticator's TOTP keys are a bit easier. A file on a laptop is even easier.
Not sure about any apps that take advantage of that yet, but the hardware seems to be there.
All iOS apps essentially do, if they store things in the keychain or even the filesystem.
If you use krypt.co, you can store ssh and GPG keys on your phone's TPM, as well as a secret key for use with a browser addon to facilitate WebAuthn. So, you can already use your phone as the "thing you have".
Apart from that I believe that TOTP keys should be encrypted and that is actually my main issue with the described tool - it stores the keys in plain, in a config file.
That doesn't change the necessity of protecting TOTP keys, session keys, bearer tokens, etc., it's just that your second factor is supposed to be a parallel factor, not an extra lock around your password.