The point OP is making is almost completely unrelated to addiction.

If someone is a gambling addict, they are going to do it. One of the issues with gambling addicts in the US before legalization is that they would use illegal bookmakers, and then get their legs broken. Legalizing is the only way to implement a harm prevention strategy because states regulators can control providers (for example, all states in the US have exclusion lists that they maintain and which providers have to implement, regulators have direct control over operations).

In addition, there is also a lot of evidence that if you regulate ineffectively, you will also cause harm. Hong Kong is a classic example where some forms of gambling are legalized to raise revenue (iirc, very effective, over 10% of total tax revenue) but other forms are banned in order to maximise revenue...addicts are the only users of underground services. Sweden have a state-run gambling operator, that operator provides a bad service (unsurprisingly), again addicts are driven to underground services.

For some reason the general public perceives gambling as both inherently addictive and something that can only be triggered by gambling being legal. Neither of these things are true. Substances are inherently addictive, gambling is not, the proportion of gamblers that are addicted is usually around 1%...of gamblers, not the total population. And it isn't triggered by gambling being legal, it is a real addiction so is present regardless.