The dutch iDeal system works like that. The merchant redirects you to your banking website where you can authorize the transaction, which tends to involve some 2-factor rigamarole, after which point the bank redirects you back to the merchant.

A more recent innovation is banks exposing this more directly to consumers. I can create a "payment request" in my banking app which generates an iDeal url which I can send by email/text/facebook/whatsapp/qr code/carrier pidgeon to someone who can then pay me. No exchange of account numbers required and the amount paid is deposited in your account within seconds.

So yes, an oauth-like flow definitely is the way to go. It's more secure and more convenient, which is a pretty unusual combination.