Yeah the rejections you mentioned are common enough in single payer systems. If there is limited availability, the government will prioritize younger individuals over older ones as young, working adults can "make back" the amount spent on care via taxes, as opposed to an older retiree who may have other complications that completely drain the system.
Whether or not one is better than the other is a massively complicated issue; on one hand everyone is covered vs those who could afford it, on the other someone you will never meet, sitting behind a desk, who might not even be medically trained gets to determine whether or not you see a doctor/medical professional. In theory a free marketplace for insurance coverage would lead to more affordable plans, however massive companies have an advantage and can corner a marketplace, as well as "affordable" plans being completely lacking in sufficient coverage.
The Charlie Gard case comes to mind, primarily that an outside entity, in this case a court, can rule that a child be taken off life support because they regard any treatment as futile, and not because the parents thought so.