Delayed medical attention is usually better than none at all.
True. However, since there has always been superior, prompt healthcare in this country, until now, your point is moot.
Ask an uninsured person in the US how prompt their medical care is. I know people living in Canada, and they love their healthcare system. That being said, it is not perfect, but many of their problems could be fixed by putting more money into the system. That is something that voters must decide though, since all of their health system is paid for through taxes. One thing to remember; they could choose to raise taxes to put more money into their health system, and they would still be spending much less than we do.
They also have a second option, and I do believe they are beginning to look at it as an alternative. Currently, private insurance is not allowed in Canada, unlike the UK. They could open up the insurance market to allow people to purchase supplemental policies. In the UK, people with private insurance usually get to jump to the head of the line when it comes to non-emergency or non-life saving procedures.