I know at least one physical casino where the tax authorities are very happy looking the other way, as patrons gamble tons of dirty cash. They do look very intently on the income and track it carefully because there is a percentage fee on gambling. Presumably that is why people are allowed to gamble freely.
I can come up with a few arguments against your idea - on the balance it is sound, but what should the limit be on "nominal"?
I can go to the cinema on a weekly basis, which with ticket prices, popcorn and other concessions can be quite an expensive hobby, or I can hit the casinos a couple times a year where I could spend the same amount of money - it is all entertainment and who is to say one is better for me than the other?
I don't know any country that has a limit on how much alcohol you can buy at a time (most have age restrictions, some have time and place restrictions, some won't sell you if you are already drunk), yet there are alcoholics in any place. Should we ban or limit alcohol to some nominal amount? If not, why should we treat gambling differently?
That said, I am all about making it easy for people to see how much they have spent, and of course be honest upfront.