Free does not mean limitless. Where I live in EU its not uncommon to wait for over a year to see a doctor on „free” insurance and less than 24h when you pay out of your pocket.
People get free insurance but hospitals get fixed amounts of cash allowing them to admit fixed amount of patients
In this scenario the answer is yes, it loses some value. Still much better system than private care in US
There is a queuing theory thing here! People die in the queue.
However the US system. seems to create a lot if inefficiency. There is no free lunch. But a lunch where you don't throw out as much bread as you eat is more efficient.