the reality that actually existing capitalism has come face-to-face with, and that to an extent is neoliberalism, is one where it's come to terms with a basic, fundamental flaw in the very fabric of it's own existence: competition is unnatural.
you have to teach kids to be competitive, they don't do it on their own. you have to create regulatory bodies to try to force firms into competing, because they won't do it on their own (at best, they might try to undercut to gain market share, but then they're in the cartel in no time. a stable market should have tiers, anyways, so that's usually harder than the simple math in the textbooks allows for.). it turns out that you need so much government to make a free market work, that you'd might as well just redistribute everything, anyways - and that the best approximation to a free market has to be almost the total opposite of the initial abstraction.
so, you don't really have this debate between governments and markets, because markets are just statist constructions that essentially give you back what you gave them (if you're lucky...). what you should have is merely an understanding of the importance of government.
and, a little wisdom should tell you that all of this energy that is created and spent on designing and enforcing markets could be better utilized elsewhere.