Yes. You can do that on Gumroad, Subscribestar and Patreon. They all allow you to block people from purchasing from you. In gumroad you don't even need a purchase before blocking someone, all they require is their email and anyone with that email won't be able to purchase your products.
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.