Like I said, I don't know the standards, so I don't know the authors' intentions. But there are actually specialized devices which do nothing but generate TOTP

Like I said, I don't know the standards, so I don't know the authors' intentions. But there are actually specialized devices which do nothing but generate TOTP tokens, so that seems to be a use case. (The keys don't have to be on a phone or in a particular app.)