It is not possible to start your own payment network.
1. It is millions of dollars just to get permits in each state to run a bank.
2. Your payment network requires users which you compete for with existing goliaths MC, VC, Amex, Discover.
3. These customers get cards from their issuing banks, which have contracts with those networks, so a bank will not issue both MasterCard and KiwiCards, and definitely not dual-purpose cards that run on either network.
4. Further, larger banks also run the payment processors, which have contracts with all payment networks. It's about a 45/45/5/5 breakdown for MC/VC/Amex/Disco. Stripe/Authorize.Net could not afford to lose a single one of those, so onboarding new payment networks which could jeopardize their business relations with larger networks is out of the question.
5. Finally, for the reasons mentioned in #4, even after KiwiCard is an established, respected, viable payment network -- it does not matter, because payment processors will have to abide by agreements with the other networks anyways. If MasterCard says Kiwi Farms has to go, it doesn't matter if KiwiCard doesn't want them to go, it will go.
You cannot, absolutely can not, fix this through deregulation. The only fixes are widestream adoption of unregulatable, decentralized cryptocurrencies or appropriate regulation of these monopolies.