One common use case we see is trust accounting for lawyers. The gist of it is that trust and operating funds are stored in separate bank accounts, depending on the context of the bill. It’s a legal requirement that can result in disbarment if not followed properly.
Another scenario we run into is with insurance billing where policy payments need to go to different bank accounts or even be handled by a different processor, depending on the policy.
I know of other software systems that can do payment routing as well.
Stripe is a flat-rate payment processor: 2.9% + $0.30 on everything.
Interchange fees range from 0.05% to 3.2%, more or less. Most consumer cards are going to be significantly cheaper than 2.9% to process. Many people use "check cards" from their bank which are in that 0.05% category, for example. American Express and the top tier Visa and MasterCard rewards/business cards are the ones where interchange can exceed 2.9%.
There are many "interchange-plus" merchant account providers now. I get better rates than Adyen is advertising on their website right now.