I confirm that this is not possible at this time - I never thought about doing it this way. Indeed, this is an interesting idea.
I think I need a bit of thinking to find a nice way to integrate it. In any case, I'm planning a major redesign of the interface starting next month so that's the right time to bring new ideas.
Note that by removing the basic Cosmic.link, you loose a number of use cases:
- Using Stellar Authenticator & other wallets to use Cosmic.link in the future.
- Using private key with Stellar Laboratory.
- Using wallet that only accept an XDR as input.
- Signing with phone using QRcodes - for example someone using SEP7/keybase on the phone but browsing the shop on desktop computer. This is a rather common situation as computers are more comfortable for browsing but phones are often more secure to store secrets keys.