I think you would probably find that to be generally the case with circumstances that are "typical". We paid tiny amounts (like $100 or something) for childbirth in a hospital. I think the bills were something like $30k or more for each one, but insurance handled it. The thing is, these institutions are set up partly with childbirth and heart attacks in mind. They sail through diagnosis, approval, and treatment. I'm glad that your dad didn't have to wait any longer than he did to get care. Heart attacks can reoccur though, so I'm not surprised that he got prioritized above other people who were waiting. When you say "skip the queue", you mean people were waiting and waited longer because of your dad. I understand the concept of triage, they probably did the right thing. What I mean to say here is that your case is common, obvious, and routine.
It doesn't take much to get out of the norm when it comes to medicine though, and when it does, you suddenly find yourself with doctors disagreeing. I at one point had two doctors telling me I didn't need a brain MRI, and one telling me that it was essential. Eventually one of them flipped and I had the MRI, which turned out to be normal. Any time diagnosis is unusual, paperwork starts to look odd, and people stop signing off. Also the immediacy of the problem can get lost when it's not something that a reviewer is extremely familiar with. This was the case with my relative. It wasn't "normal" so it didn't sail through, it didn't get recognized, and her day-to-day coping wasn't considered to be on par with what other people were deal with. So she was given a back seat.
It's tempting to say that she should have been given a back seat, since other people were more important. But the only reason she was given a back seat was the the government's healthcare budget was set, so if more people need care, they wait.
All of this also greatly diminishes the impact to someone's life that sitting around with a non-life threatening injury can have. Needing to get around in a wheelchair and in pain for a year while you're waiting for knee surgery can have a huge impact on your life. And it's just not going to rise to the level of priority that a life-threatening emergency can have. So if you have a fixed healthcare budget, some of those knee surgeries get put off. And people truly suffer because of it.
Healthcare is a personal decision. It has to be. You're the only one who can know what it is worth, and whether the money should be spent now, or you can wait for care.