If there's more than one grocery store, I probably get better prices. (Or, negatively, if there's only one then I probably get worse prices.) And so with every other aspect of the economy.
There are several hospitals around me. Endless amount of doctor offices. There are several health insurance companies I can choose from. There is competition. Yet, prices are not affordable for most.
it's because the number you're comparing to is from other countries, where they subsidize their own citizen's healthcare.
The US's healthcare system has become a convoluted mess, and the competition you mention is not sufficient.