The reason the government contracts with private healthcare companies is because it knows they can deliver it more effecienty, profits and all.
Most federal employees I know have government paid Blue Cross/Blue Shield plans.
One of the mantras circulated during the last presidential campaing was that the governments costs of handling claims (Medicare) was so much less than private insurance companies.
Problem is, the government doesn't handle any claims. They use Medicare intermediaries ( private insurance companies). See above, and quit believing people like Jim McDermott, John Kerry and Al Hunt.
And if you think healthcare costs a lot now, just wait 'til it's free ( P. J. O'Roark ).

Just as the English language is comprised partly of words of other languages into what we call the English language. So, too, can we incorporate other systems into our America without fear we have become that system.