The site could block their PayPal or credit card.
Is there maybe an example of a storefront where you can upload and sell your things to the public, but block individual customers? Just curious, because you called it a basic privacy and protection service. Selling to the public usually entails selling to anyone that pays, not anyone that pays minus some people.
If you have reason to believe and maybe proof, that someone abuses Itch, you should contact support. Should they agree, they might do more, than just ban the account from buying your projects. Especially, if the account should abuse refunds.
Sounds useful. Especially the pre-blocking on Gumroad.
Of course this could be easily circumvented by any dedicated unwanted customer. Especially on Itch, where you do not need to create an account.
Which might be the main reason why this feature does not exist on Itch.
Also, I have contacted support about this in the past and they say they don't block people even with evidence of these malpractices. Itch.io doesn't care.
Oh, I think they do, but they probably can't. Banning accounts would be something for violating the terms of service. And those regulate only things that happen on Itch and not things that happen, after something was downloaded from Itch.