They do NOT want to involve Visa, nobody does because Visa has fees and they are another layer of liability for the banks to worry about.
Fees that are lower than the cost that each bank had before 1965-1970 when they were operating their own card, and lower that what they would have to spend if they were still operating them.
And it's not limited to the fact that Visa ~30,000 employees do the job that each bank would have to do internally, and therefore saved them around ~10,000 employees each. It's also regard the research and development, as well as the implementation of innovation that come from others entities (introduction of IT systems early 1970's, electronic authorization late 1970's, holograms
(now abandoned), magnetic strip, and ATMs mid 1980's, PIN validation late 1980's, online processing protocols early 2000's, then RFID no contact not so long ago). Something that, here too, would have been at the charge of each banks, costing them millions each in R&D, then other millions to see it adopted, then for the less lucky, again millions to switch to the solution that became the standard.
I'm probably among the few old enough to remember this, but there were a time where owning a card wasn't at all seen as something interesting. It doesn't removed the need to goes to one of your bank agency when you wanted to get some cash, and it wasn't easier than paying by check; it just took less space to carry. The good old machine taking the imprint of the card, imprint that you had to sign while showing your ID. Probably more can remember the times when you needed to sweep your card through the magnetic reader.
All this had a cost for the banks, and they weren't the ones that had to spend money to find faster, more effective, more secured, and less expensive, alternatives. It's banks consortium like Visa that spent the money and found agreement for a solution to become the standard. The money that each individual bank lost in fees for Visa or MasterCard since they joined one or the other is lower than what they would have had to spend just to stay in touch with the technology evolution.
As for the layer of liability, it too have two edges, presenting a potential risk on one way, and a security on the other way. Something that is especially important nowadays since it serve at central point for the transactions, whatever if they are online or real life.
You can potentially doubt of the legitimacy of any IRL outgoing transaction, but incoming ones come from a trusted source. This while for outgoing online transaction, banks have their own controls over them. If you don't have a second factor authentication operated directly by your bank when you pay online, change your bank; a modulo here, smallest payments (for me it's below 20€) don't have the second factors, and a site can join a bank's trustworthy list by complying to their strict security conditions and frequent control/pen-tests.
By the way, this doesn't limits to the fraud aspect. There's also the whole numeric traffic that play a role here. There's a gate open for it on your own systems, and it's a fucking vulnerable point. Having to open only one gate, and for a single entity that you can trust, is obviously better than having to open highly controlled airlocks for thousands of banks.
By definition, Visa/MasterCard are a central point, the gate through which each card transaction have to pass. And securing a single gate is, and will always, be easier and better than having to secure thousands of different gates; it will also always be cheaper since you've to pay a fraction of the operating cost for that gate, instead of the totality of the operating cost for thousands of gates.
All this is the reason why banks are happy to involve Visa/MasterCard, it save them millions to billions
(depending on the size of the bank) each year, even counting the fees.
If they weren't, they wouldn't have joined the consortium in the first place, they would have continued with their own card, and our life would be a mess. They also wouldn't have grouped at national level to create their own consortium in order to operate the local transactions, like many banks did.
Visa has an entire industry by the balls and no, there is nothing anyone can do about it.
They can switch to MasterCard, American Express,
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,
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,
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, and few others. Or they can create their own entity, like
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. So far EPI is more a sleeping entity than an active one, because the threat isn't big enough, but it's fully operational and already act as secondary layer for some transactions implying European banks.
Thinking that Visa is all mighty is not knowing how big and complex the banking system is. By example in France we have our own network for banking cards,
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. All national card transactions are handled by it, while internationals are handle by Visa/MasterCard
(depending on your bank), with still CB acting as hidden layer between Visa/MasterCard and the bank. And it's far to be something exceptional.
It would have a cost, and wouldn't be immediate, but CB can turn international if Visa decide to goes too far. This even if it need at first to rely on an entity like Stripes or PayPal to handle the online transactions, the time for online shops to implement the handling of their service.
There's a limit that Visa can't overpass without risking to loose partners, and even them know it. This simply because being the biggest consortium doesn't mean, far from it, that they are the only one.
Even politically, Visa and MasterCard can't goes too far. It would create a risk that UnionPay
(China) grow to fill the gap. A risk that the US government, whatever if it is red or blue at that time, can not afford to take. The instant a big enough bank would threaten to leave Visa consortium due to a move made by Visa, the head of Visa would receive a call from the White House telling him to stop being an idiot.
A reminder too that adult content is not banned by VISA, it's accepted on onlyfans after all.
More than "adult content", the fact that Visa is a partner of OnlyFans is the demonstration that sex works is not banned by Visa.
What Visa don't want to deal with is prostitution, because it's illegal, they would be held liable, and all. But as long as a platform can offer them the guaranty that there's no prostitution, and provide the security deposit to cover the frauds cost, they are happy to deal with your sweet money.