This has nothing to do with the actual gambling sites themselves and relies far too much on self control, which any addict will tell you is their major flaw. The answer to self exclusion from anonymous gambling sites is simple: if they truly are anonymous then they should never have access to any personal information and this would preclude them from being able to effectively ban you. In that case, the most they could do is place an IP ban on you, which they may be hesitant to do because it could restrict other legitimate users as many IPs are shared these days. It's simply not a solution or practical for the people you suggest.
I understand your view and proposition but no matter how you try to suggest a solution, there will always be flaws. Fine, they can't be able to exclude the addict if they are true to their anonymity, but I see the same flaw in placing an IP ban on the gambler. This is even the simplest of it all if the addict is using a dynamic IP. It is as simple in my country as just putting your data off and on, the IP automatically change to another.
But I like your additional view, who knows, another customer without issues living in the same country will soon be a victim of the IP ban, so it's pointless.