1. Gambling in fact has many negative externalities. If someone gets addicted, the likelihood is much higher to be depressed. Depression is factor, which leads to high costs for the society.
2. Gambling addiction leads to economic costs because of crime actions. Other market actors have to increase their security standards, which means higher costs.
3. Many gambling addicts go as a consequence to jail. Jail means EXTREMELY high costs to society.
What are your thoughts on this topic?
While I do mostly agree with the points you raised, the claims that you made are all fallacious, being a slippery slope.
Any addiction caused to a person has always its negative externalities, not just gambling. While gambling may be considered one of those addictions that are common, you must also consider those other addictions as they contribute to the costs in society.
In addition, while those negative externalities in gambling are present, you cannot escape the fact that gambling brings revenue to the government. The revenue garnered from these gambling establishments enable to government to construct infrastructures which bring positive externalities as a result.
It is thus, imperative to know where to draw the line on how to balance these negative and positive externalities. While the result of gambling addiction is detrimental to the society, we also cannot disregard the financial aspect on how it brings revenue to the government.
Short answer: OP is right and there is absolutely no way the tax raised from gambling could cover the costs society incurs due to gambling/addicts.
Long answer: it requires extensive and fundamental research to actually come up with concrete numbers.
Especially online gambling socially isolates the players. One could argue that the five friends playing poker in the garden having a barbecue is even a net positive to society because of the recreational effect. How recreational the effect still is to someone sitting alone in front of his screen, I don't know.
Anyway, the topic is certainly interesting and a very good idea to look at it from the angle OP brought up!