Many U.S. credit unions are members of CO-OP Financial Services [0], a cooperative of cooperatives, which provides shared ATM and branch services. Effectively making it one of the largest networks in the USA. There are other similar organizations that provide various backend and federation services.

[0]: https://www.co-opfs.org/About-Us

The entire US payments system is a co-op payment network[1]. The Federal Reserve is owned by its member banks and they handle clearing for some absurdly large number of transactions. They use a slightly different nomenclature, but pragmatically it's a member owned co-op.

[1] https://www.federalreserve.gov/faqs/about_14986.htm

I don't think a global association of lyft, uber, didi, grab, doordash etc is exactly the kind of 'coop' that these people are going for. Your describing a coop of large organizations. This is a 'by the people for the people' type of organization, which the closest thing I can think for is a credit union.

Fraud from either side of the transaction is the primary issue payment networks deal with and that makes them a poor fit for coops. Ride sharing apps are very different beasts.

Which suggests non-coop payment networks are more successful in the market. It does not tell us anything about whether they are actually better for anyone.