Have to be one more person to join opinion that banks really can't be suggested to watch and block legal transactions people are making. When getting to that point that gambling problem is so severe, very efficient way in it is cut source to money, someone else can assist and hold access to persons account and only certain very limited amount of money would be available there for spending (where ever want it to be, for pints with friends, small shopping, eating out or even gambling) and all the other money for rent, bills and other important mandatory stuff would be behind of someone else.
Like suggested here earlier, it can be possible to block certain gambling transactions but that's probably not very bullet proof as person still have access to money and buy paysafe or other pre-paid cards or find way to circumvent these blocks quite easily. Like spoken in Gamstop and other self-exclusion topics, when person get in so big troubles with gambling (or some other addiction which is too strong to control by person him/herself) that these blocks just don't help anymore as there is always way for you to gamble if you have money. You can even find people who create account and deposit for you when you give cash etc... Way to do that can be found if will is strong enough.
For these very serious addictions blocking something or blaming that somebody should have stopped person from doing something, like depositing and gambling, which is not very strange thing to do which should flag everywhere high risk behavior and should be stopped. Like pointed out, these kind of actions would make majority of people who haven't got addicted for gambling to get very inconvenient situations when their money transfers would be blocked and returned after many business days, all the banks and payment providers wouldn't be able to serve people how they should when people want to use own money.
These addicted people should be helped and look for support which i hope is available. It's long and very hard to comply with such severe addiction but due that it also needs very stong approach and start from point where there is no access to money, strong support and safe net built from everywhere it's possible and try to get on with that. It's big change to life to get out from addiction and many need really strong support like this, but when you are in situation that it's only way, then it pretty sure is worth it.
When claiming banks, casinos, failing GS etc.... what ever is reason for failing when trying to be wihout gambling, it's still pretty much denial of addition to be that stron what it really is and trying to take easy way out by extending responsibilities to others but unfortunately it's not working like that for longer period, if person can't control habbits which cause so big damage, then admitting problem and reaching much support as possible is usually pretty much only way to help. As long in denial state and claim others to fails when trying to control addiction, real work trying to control it and live with that is not really done yet, but unfortunately need to take one step deeper to be ready to fight against it with all possible ways.