It is true that the casino can check all of their members and they do that too for security purposes. But while it is a matter of tax I think gambling sites should bear the tax of their end which they earn only. And for the users, the users are liable to their country whether they will pay or not.
The tax for the casinos and the gamblers are different. The casino must paying the tax for their business while the gamblers pay the tax for personal or their wins. But gamblers should pay the tax for their income/salary as a citizen.
I am not too understand about this tax matters as I am not the officers from the government so the tax matters can be different between each countries. If you wants to know more about that, you can visits to the tax government office and asks to the officers about that. The closing of the online sites can be a good way to start controlling the online casinos.