> No need to use something like stripe.
Why wouldn't you consider using a third party (no idea if Stripe can actually do the example described) as true innovation in this space? With a third party layer, banks don't need to reinvent the wheel.
> Got a deposit via Venmo? It goes to X. From your work? Goes to Y.
FWIW, this sounds analogous (not exactly like) N26's closed/semi-closed digital wallets[1]. I guess if there's a use case for the example you proposed, it's not a huge leap to go from here.
Alas, I'm a very basic bank customer so I can't vouch for how good this feature is right now.