I prefer not to have beaureaucrats decide how I spend my money.
I've had a relative with a treatable condition wait so long for a surgery that her condition worsened and it couldn't be fixed and now she is permanently physically disabled.
They do the best they can with the budget they're given.
Private hospitals and health insurance are still allowed. Here in Canada, every public hospital still has a billing department for the uninsured & those with private insurance (foreigners, etc.) (I wonder if you can opt to pay to "skip the queue" here?)
What you're talking (skipping the queue) about is a two-tiered system, which I would be in-favor of but it is taboo to even bring it up in Canada (or at least, that has been my experience).