I very much doubt that people will even want to give out information about themselves that they actually play gambling games in online casinos. In society, as a rule, there is a bias towards people who play in casinos. Therefore, in some cases, even the fact that someone will know about your online casino games will be enough for a person to stop playing in an online casino.
Government or any public or private organization should not intervene or interrupt in any activity that people are doing that may have a bad impression in the public, the general society has a bad impression on gamblers and this will discriminate them, they can just pose serious warnings but it's on the person to imposed it to himself not the government.
Government intervention in people's Affairs is a complex thing. Here it is important to observe a fine line, how to set the rules of the game and not directly interfere in people's Affairs. It seems to me that it is impossible to set limits on the amount of loss so that they do not affect anyone. Someone can afford to lose tens of thousands of dollars and still not get serious damage to the wallet. And for someone, losing a hundred bucks will already be a serious loss.