It's because Visa got sued, lost, and it was found out they knowingly processed payments for illegal adult content, so they basically avoid the sector entirely now. Economist had an article about it maybe two years ago and came to much the same conclusion you did. IIRC, the failure in their mind was government not stepping in to make a law so things are less ambiguous in the future. Now payment processing cos get to gate keep people's speech, which means everything is basically a civil suit away from getting blacklisted.

Because they are on the hook for fraudulent transactions, until they get to merchant to refund. Otherwise they wouldn't care.

Which is why some merchants get effectively blacklisted if they have too many fraudulent transactions

Well your comment tells us why-- as is the law in the US is that credit card companies are almost entirely responsible for fraud. It's part of why they and their dubiously usurious practices are allowed to exist in the US at all.

If it were the case that the payment rail censorship were limited just to cases where there was an obvious elevated fraud risk-- then that would be the whole of the story. -- and there would be an obvious answer: use a payment mechanism where the fraud responsibility is entirely on the user, such as Bitcoin.

But their censorship exists where no such elevated fraud risk exists too, due to abusive conduct by the government to indirectly suppress activity that would be plainly unlawful for them to directly suppress. And the governments out of control abuse of its regulatory power is not limited to fraud-responsible payment rails, and get applied just as or even more extensively on Bitcoin payment processors.