I think your position is reasonable, but I would like to point out that the reason the free market has not been sufficient, as you say, is because it hasn’t been allowed to be. Government regulations have stifled it.
Think about all the areas which the government hasn’t (yet) completely taken over; those areas are doing pretty well. Take technology, for example Companies like Apple produce the most amazing technology the world has ever seen, because they are made up of intelligent, hard-working individuals who are allowed to operate in a free, stable market environment. That’s a perfect example of what a truly free market can do. If the free market “doesn’t work,” it’s because it’s not allowed to actually be a free market.
The government hampers the market with excessive regulations and taxes, and when the market buckles under the weight, the government says, “Look, the free market failed! That must mean we need more regulations!” and they persuade people to give them more and more power. That’s exactly what they want.
I’m not intending to come across as angry;

I’m just explaining why, as you pointed out, the free market sometimes appears to “fail.”