You are talking about a many-to-many relationship here. Every payment processor has to ensure their system works with every bank, and vice versa. So the standard defines the data format, great. What happens when Payment Provider #223 has an issue communicating with Bank #16252? On an even bigger scale, who is going to maintain all of the necessary technical info for the parties to all interoperate? Who will handle fraud detection? Who will be liable for fraud that goes undetected?

Credit card companies handle all of that and much more in exchange for transaction fees.