I would recommend taking a look at ZenGo. It's the first keyless, non-custodial wallet based on threshold cryptography. There is no private key but you're still the ONLY one who has access or control of your funds.
Look great, I start to searching about ZenGo and found articles on
Mashable, there is mentioned if we need to scan our face to start using wallet after registrations.
To backup your wallet you do need to scan your face. Although the way that the server side stores the face scan is through an encrypted mathematical representation of your face (not an actual photo). So it's not something that could be abused or distributed.