Price caps play a role, but rationing plays an even bigger role. Google search for the McKinsey paper on US healthcare costs. The volume of outpatient procedures in the US is quite shocking compared to other countries.
Yes, things cost more in the US, but the volume is also quite a lot higher.
In your parent post you mention outcomes, and that's a really important thing you're missing when you talk about "rationing".
If a scan is more likely to cause harm than to treat illness is it really being rationed, or do single payer systems have an easier time not providing harmful over-testing and over-treatment options?
Yes, things cost more in the US, but the volume is also quite a lot higher.