Also: yes, building a government blackmail database is draconian.
Except on the largest of the sites which was successfully sued just a year and a half ago over it's years-long policy of looking the other way.
I'm no puritan, I'm just not an absolutist. The real world is complicated and I find arguments like yours annoying and naive.
First of all, not all NSFW transactions are created equal. A person subscribing to a website, a person buying a physical product, and a person paying an artist to draw what they want all have different risk profiles. (The former is far more likely to cancel). Does this change the opinion of Paypal, Visa, Mastercard et al? No, they blanket ban everything. They pressure businesses and platforms to stop selling this content and to cut out any of their NSFW creators, and the websites often have no other option. These big companies are the only available avenue for sending and receiving money.
Second of all... I think that being free to do legal transactions with whoever you want in exchange for anything you want should absolutely crush the payment processors' right to moderate their transactions in accordance to their own guidelines, rather than the law. Again, you have almost nowhere to run if these businesses turn you down - there is no digital cash. I think that companies that process transactions should be mandated to not discriminate between them, as long as it is lawful.
Lastly... The reason why this verification debate has been standing for 25 years is because it's not solvable. Every proposed scheme for reliable age verification that I've heard of either trades off your privacy, or isn't watertight (and might as well not be there). You can only have one. Given that private companies and governments love private data, and that we've had open internet for 30+ years now and nothing catastrophic has happened so far, I say we should let it be.
An enterprising PM at a PSP or fintech could look at the size of the sex industry, measure the risk of providing payment/banking services to sex workers and businesses and offer them at a premium like any other "niche" financial area.
And while we're on the topic of "draconian" regulations from the government - it's not outside their interest to limit the availability of obscene content from children. This isn't a "think of the children" argument so much as "children consume graphic pornography at huge rates and porn providers make money off them as consumers and producers with such inept guardrails that age verification has been a meme for 25 years." I don't think validating your identity with a government ID (and storing it forever) is a good countermeasure but I disagree its some kind of draconian limitation on free speech. If porn sites didn't buy and sell sex from kids and self regulated, this wouldn't be necessary (nb4 "it's the parent's problem" - good luck!)