My doctor wanted to give me an MRI for a pain near the heart, and insurance told them they wouldn't cover it until they did various other forms of cheaper treatment, including taking antacids for one month, and 5 months of physical therapy. Which of course didn't work. The waiting time for the first appointment was 3 months.
It took over 9 months for my doctor, the only person to actually properly know the details of my case, to be able to give an MRI that he thought was necessary because someone at the insurance company, who I never met, who had less medical expertise than my doctor, wanted to save the insurance company money.
Anecdotally, all the people I know who live in countries with socialized medicine haven't ever had a wait time as long as that, and haven't ever had a simple MRI be delayed by their socialized insurance.