Denmark has been moving in that direction. Its overall level of safety nets, taxation, infrastructure spending, etc. is
much higher than in the U.S. (tax revenues about 2x as high, as a percentage of GDP). But in some ways it's actually more privatized: for example, the bus system in Copenhagen is bid out to private corporations to operate. The government comes up with the fares, set of routes, etc., and then the corporations bid on how much subsidy they'd need to operate under the specified parameters (Movia won the current contract). Whereas, most American transit systems are operated by city or state employees.
And: it's fairly easy to fire someone, certainly easier than in most of the rest of Europe. The compensating factor is that the social safety net for the person who gets fired is also quite good, and not just in monetary benefits, but in active assistance to help them find a new job (both through job banks and training/internship programs). Incidentally, that is also outsourced, with a number of private (though subsidized and nonprofit) "a-kasse" social-insurance organizations competing for members. I'm a member of one that specializes in researchers, for example. If I become unemployed, for the first two years I would deal with them, not with the state. That tends to lead to people joining the organizations that they feel will provide the best job-finding assistance. Some element of competition is introduced, since a totally useless a-kasse would (hopefully) see an outflux of members.