I think I see what you are saying. You would like it so that if I wanted to send money to you, despite not knowing you or knowing your details, I could select you from a central repository of bank information where your details are stored?
100% no from me! I do not want my details stored so that people I do not know have access to them. 200% no to storing them in facebook or any other social media related account (including whatsapp).
By mobile number already exists, called Paym.
As proved my Payms low sign up numbers I would not expect this to be very popular.
Personally I also have no interest in signing up for yet another app/service, and it would seem that a lot of people feel the same.
Other people may feel differently of course.
The worst that would happen is the money would bounce back (AFAIK), or be redirected if they had opened a new account via CASS. The former of which would just mean you ask them for their details, which is fine to me.
I will say again that, for me, If I was B and A paid me, I would NOT want C to be able to have access to those payment details without me giving them to them - I have no idea who C is or what their intentions are.