You could implement a compatible API, but it turns out that consistent distributed payment systems are a hard problem, and blockchains are a solution to that.
There's distributed and there's distributed. Blockchain might be overkill, but it solves the "JPM's transactional database of financial transactions is down" problem.
The benefits of private transactions without notifying the processor (and circumventing financial regulation, or at least delaying it), is immediately obvious. It's a distributed payment system. The control you mention, is subjective.
There's no reason to add the problems of distributed data to your payment systems unless you HAVE to.