There exist similar systems in pretty much any other western nation. The problem is that teaching doctors is expensive and isn't something you can ramp up quickly because you need other doctors to teach the new doctors. The supply of doctors is a problem that is universal to essentially all western nations especially if you move away from metropolitan areas. It's largely due to aging populations and failure to increase spending on medical education over decades. I think the US is actually better off than many other countries, because they pay disproportionately high salaries so get more immigrants.

That said I don't think there's evidence that lack of doctors is what is driving up cost in the US. Just an example, growth in hospital administrators has significantly outpaced medical staff over the last decades, which will directly increase cost.