Most of the problem gamblers in this country are poker machine players anyway, and if people with gambling problems spend their money on the TAB, it's highly likely they wouldn't have online betting anyway. Sure, it's more convenient, but to make a bet you actually have to have the money sitting in your account first, which involves either going down to the TAB or doing it via BPay which takes at lest 24 hours. Problem gamblers don't want to run around like that.
The accounts with credit cards - well think about it. To get a credit card, you have to be on a solid income and have plenty of assets, especially in this day and age. You've also got a set credit limit, so in a way there is a restriction there isn't there? You can't bet over your credit limit, and most people who use up their credit limit on credit cards (whether it be via gambling or not) can still make a minimum monthly payment pretty easily.