Also, I don't know that we have to ban gambling. I don't think people having the occasional poker game is a big problem. It's industrial-scale exploitation of addicts that I take issue with. I think it would be sufficient to ban profiting from gambling.
My experience is with 3rd world countries, specifically Thailand, where gambling is illegal. I know you're not advocating for a ban on gambling but I think it's worth a mention that due to its illegality, there are widespread issues that stem from it: corruption, cops being in on illegal gambling dens, and mafia / gangs that sprung up to run these under ground dens.
Aside from the more organized underground gambling, there are also smaller village style gambling where within a village / town / city, there are bookies that will collect your bet (and people bet on anything: soccer being the main one.) Basically addicts will find a way to gamble whether it's banned, discouraged, organized, or legalized.
In the case where it's illegal, the creditor who the addicts borrow money from are usually loan sharks or gang members that take extreme means to recover any money they can. Many families lose homes, life-savings, or even get killed. So it gets pretty bad, IMO it's worse than a legalized gambling system.
People who wants to gamble prefer to go to the legal means as it pose much lower risk of extreme repercussions... but if it's not legal, some of them would still find a way to gamble. This may mean that the number of people who do gamble reduces... but I'm not sure by how much and whether that ends up tipping the scale in favor of a ban.
So as far as I'm concerned, gambling should be legal, as I don't want addicts to ever worry about coming forward. And if somebody wants to be the office bookie as long as he pays out every dollar he takes in, hey, have fun. But the moment somebody has a profit incentive to hook people and keep them hooked, I think we've created a very dangerous situation.
This part, though, I take issue with: "Basically addicts will find a way to gamble whether it's banned, discouraged, organized, or legalized." That's somewhat true for addicts not in recovery. But I think it ignores people in recovery, those getting started on recovery, and those with addictive potential who aren't yet addicts. For those people, availability all matters a lot.
We've managed to reduce smoking a great deal without black-market tobacco farmers springing up. There's no reason we can't do something similar with other addictive products.
I do think that eliminating the profit incentive is something that could work. The profit from gambling is cited as a redeeming quality, however, as a reason for legalized gambling to exist. The overwhelming idea, at least in the US, is that if people are going to have a vice (or fun, depending on your perspective), their activities should be taxed so that others (corporations and the government mainly) can profit from them. Perhaps if the money actually went to fund schools and other things that benefit society, I could get behind this viewpoint, but regardless of the claims of governments that have legal gambling, it doesn't. This John Oliver segment about it is pretty interesting: https://www.youtube.com/watch?t=789&v=9PK-netuhHA
I definitely agree with you that the society-benefit line is mostly a sham. With cigarette and alcohol taxes, the general goal is to discourage consumption. But many US states actively promote gambling, so I think it's a very different thing.