Up until a year or so ago, an appointment at a GP would take weeks of waiting. Specialist appointments were 1+ years waiting time. This is somewhat better now with the establishment of critical-care clinics operating after hours. This is from personal experience.
The emergency rooms often had waiting time of 12+ hours(or more). I know someone who has been waiting on a procedure at the public hospital for 6+ years. Another has a child waiting for an appointment with an estimated wait time of 3+ years. All non-urgent but a wait list in the years is no longer a wait list to me, it's a system that is not fit for purpose.
Initially all of this was attributed to the pandemic and the harsh lockdowns in Victoria. But a few years out, it seems difficult to still do that. When asked, our government just re-states that they've invested in this and that and then deflect. Recently, due to the horrible state finances, the healthcare system was being downsized with services cut and the bloodshed continues. This is without talking about the systemic issues and incompetence I've seen.
The funny thing is that outsiders think that public health care means free. It's really not. We pay for it on top of our income tax(1-2% on top, more if you're above a certain threshold) and it is not cheap. It wouldn't be so bad if it was working like you'd expect but paying for a non-functional system is....I don't know what to say.
Emergency 12+ hours wait is not an ordinary situation - could be when there is a combination of very busy night (like Friday during long holidays) and lowest triage category. Every time I attended emergency I was almost immediately triaged and when things were serious, was admitted in minutes. When it was just a cut with bleeding stopped, I was advised after triage that I can wait for 4+ hours or just come back in the morning. All my friends had the similar experience with Melbourne's public hospital ERs.
2% medicare levy is cheap compared to taxes in other countries with free healthcare.
I'm actually very surprised that someone has such negative impression about Melbourne's medical system. There was a short period several years ago, related to COVID, when ambos ramping time could be hours, but that's not not typical for Melbourne, and was resolved pretty quickly.
I do have to state though that the US healthcare system, minus the fact that most healthcare research/advancements happens there, is crazy.