You are right, it was a long time ago. But the 1975 system was brought in the by the Whitlam government was only universal in that it brought in a single payer system, but not free and not unrestricted. (Before that we had a hodge-podge not unlike the US before the ACA.) After the coup against Whitlam, the subsequent government further restricted or watered that system down, until Hawke brought in a universal healthcare system in 1984, medicare.

Still, with each period of right wing government in australia, we still seem to get a slow death by a hundred cuts to the medicare system (medicare levy, indexation freezes, closing of bulkbilling clinics etc etc etc).