You can watch this video from 07:20 if you want to skip on the other parts:
https://www.youtube.com/watch?v=sxty2XhTwVIBasically it's very simple.
You take a currency that requires 21 days for staking/unstaking, then you deposit this amount in Atomic Wallet, stake it and then you can't gamble with the crypto you're holding.
The locking (staking) is done with one single click of a button, and it's practically speaking, equivalent to activation of self-exclusion on an online gambling site with a click of a button (and yet not all sites offer it unfortunately).
For example, you stake (lock) $200 of your crypto, and that's all crypto available for you - then you can't play/gamble/risk it for at least 21 days ... do it 15 times a year time after time, and you would be excluded for a long time.
The only drawback with this method is Atomic doesn't offer this on USDT so some "gamblers" might not like this idea because they trust stablecoins more than other crypto coins, but this is FYI.
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.