That's not nearly true, at least for Melbourne as a metro area. I never heard of weeks waiting for GP appointment, and I never waited for more that 2-3 days for GP both in east and west suburbs. Usually you have at least 3-5 GP medical centres in 5 km radius, and in half of them appointments are avaliable same day or next day. That's the case now, and was the case 5 and 10 years ago, with only obvious exception during COVID. 6+ years wait could occur, but it would be ~1% of elective surgeries. Basically, elective surgeries are covered by private healthcare, that's the unofficial limitation of Medicare. I got an elective surgery twice, wait was 4-6 months. Just to stress, that's an elective surgery fo non-life threating condition that just affect your quality of life, so it's reasonable to expect people paying up private insurance/hospitals for getting this done quickly.

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.