I don't think the payment processors directly want control. This probably was just a case of them wanting to avoid lawsuits or smear campaigns that can hurt their revenue (or maybe the leaders of collective shout had direct contact with those payment providers?)
There's tons of companies trying that already (like fucking palantir).
Why wouldn't they want control. Visa and mastercard have a market share of around 60%-70% worldwide already. There isn't anymore money to me made by them because they have saturated their market. With this amount of money they have such a massive lawyer section no one would dare do sue them.
The only thing the are missing is control to protect their current market share.
Kodak tried to do it with banning digital cameras.
Nintendo tries to do it with while game genres.
That's why we now have to deal with so many subscriptions instead of one time payment products.
Customer control is the end goal of all companies. That's not even a secret or a conspiracy. That's what being taught in first semester economics in universities.