Like it or not, part of the baggage of doing that service is being an extension of the long arm of the law.
So "rolling your own" minus the regulatory baggage you don't like, isn't per se "making your own payment processor", but something else.
Bit of a Catch-22, but how it works. Everyone just tends to leave the quiet part unsaid.
Pornhub essentially is already their own payment processor, as it looks like they are processing cryptocurrency payments from the customers.
If Visa loses, payment processors have little choice but to remove processing from sites that allow user generated content, including Reddit. They are legally responsible for all under-18 content, and as "Big Evil Corporations" they have no support from anyone in the community that matters.
The EU and UK is even worse in this regard, so no anonymous commercial social networks will ever be created again.
Yeah, many creators and pr0n companies will tone down their content. But we all know that consumption of pr0n doesn't lead to more vanilla tastes. The more "deviant" acts will find ways to make revenue outside the mainstream and then all it will take is a critical mass for some digital currency to mean something.
Making it Visa's responsibility forces them to be proactive. We're dealing with a case of illegal porn involving underage victims so I think that makes sense. Mindgeek has taken steps to fix the problem but maybe Visa isn't convinced that they've done enough.
By allowing policies that crack down on the entire sexwork industry, more women, children, trans people, etc are hurt, than are hurt by the actual criminals making child porn or sex trafficking. When everything goes underground and there is no well-regulated marketplace, people get exploited and abused. There's hundreds of interviews with sexworkers who all talk about how their work is more dangerous now.
Pressuring Visa makes all porn go underground, which includes child porn and trafficking. That leads to more harm, because there's no visibility and no protection.
If we didn't pressure Visa, and instead had a flourishing open market that was monitored, regulated and policed, it would be easier to notice the illegal activity and move to stop it. A Department of Sexwork could work directly with Visa and content creators to develop sophisticated methods to identify and stop illegal activity.
But since it's harder to see abuse when everything is underground, politicians prefer it that way. If you don't notice the abuse happening, must not be happening; problem solved. No US politician will get voted out of office for banning sexwork, and Visa's bottom line won't get hurt either, even if it does result in more actual harm to people.
The whole stack includes the merchant, the payment processor (think CyberCash, Authorize.net, PayPal, Stripe, Verifone, NCR, etc), the merchant bank, the card network, the issuing bank, and the customer.
If the card network won't deal with you, you've got to build your own card network and issue cards or convince customer banks to issue cards, and convince processors to process them and merchants to accept them etc. I don't know how many adverisers PH has, it might be easier to just ask them to write checks.