Take energy or water, for example; the amount of kit/ownerships needed to actually start in the industry is so vast that basically any pretence that a free market is operating is a bit of a sham. In terms of assumptions, a good example would be that neoclassical and classical economics both assume perfect knowledge, which is clearly bullarmadillo and makes a lot of difference at the consumer end. It's often simply not the case that the market allows the most superior, cost-effective product to win out. As you rightly say, we can trust businesses only to try and make money. Why, then, would we trust them not to be doing whatever they can to avoid having to produce the best goods for the best price? Their whole raison d'etre would imply they should be trying to produce the cheapest goods and selling them at the highest price that they can get away with, and the market can't always fix that when you take into account that people have a lot of reasons for buying products other than their actual cost-effectiveness.
I guess my view is that the market is a tool; there are some problems you can solve with it, and there are some things it's damn good at. For many standard consumer goods, competition can be fairly good at encouraging innovation and pushing prices down. The downside is that there are a lot of places where market solutions just don't make sense. These especially occur where goods are very basic, hard to have competition over, represent a "public good" where we can save money by just bulk providing them for everyone, or some mix of the above. I'm not actually a massive statist generally: I don't like the idea of too much power being concentrated in the government's hands. But I do think we need to be even more wary of businesses, not least given it's significantly harder to get rid of them.
