I can't get a credit card anyway since my income isn't high enough, and I wouldn't want one because they charge annual fees in Australia.
Banks in Australia run their own payments system, so it's possible to pay by card without going through Visa / Mastercard. Some cards issued by banks don't even have the Visa / Mastercard affiliation, but I think the Visa / Mastercard debit feature is needed it you want to make card-not-present transactions online.
They generally don't have any kind of linked reward points structure, but that's not a huge loss as most of those got nerfed after the ACCC changes a while back (see elsewhere in these comments).
I do have a Visa DC and a MC CC for redundancy if my bank is down, most people I know doesn't even get why.
(Seriously, people, these kind of statistics are extremely easy to find. No need to make them up!)