This might help, but gamblers have a loophole on this one.
They'll just register to multiple licensed online gambling websites and they'll play on them.
If they reached the limit on their first site, they can just move on, and go to another website, and so on, and so forth. Also, I'm thinking of using another set of personal information (assuming that there's a KYC), as another loophole. I mean they'll just create another account using their relative's name, and they can gamble again. While this might help, they will not solve anything significant at least from my perspective.
I personally don't believe any online casinos limit players' play, such as limiting them to a certain number of times a day. But if such a casino does exist, then your statement is correct. Once a player reaches their limit, they will likely move on to another casino if they still want to gamble. Furthermore, I believe that while these casino options may help curb gambling addiction, this isn't guaranteed. I believe addicts will still find ways to gamble again, especially with the many online casinos available and easily accessible. As you said, this might help, but it won't completely solve the problem.
Even if the government issued this warning, it wouldn't have a significant impact; the problem lies with each individual, who has a different perspective on gambling.