But Communism != Socialism.
Socialism is simply Communism-lite. The difference is quantitative.
Socialism certainly does allow for a reasonably free market.
Socialism/Communism can be measured — the measure is the percentage of the country's GDP, that is spent by the government. The US is at about 50% these days (once you add up Federal, State, and local government spending), which is terrible.
Other countries have more or less. At some point — I'd guess, at 90%? — it can be said to become bona fide Communist.
It just makes sure that said free market doesn't fuck over the people
Yes, yes. I know, Hugo Chavez was great, was not he?
detrimental to society to simply hand over to the free market, such as roads and healthcare.
And the Internet, and food (can't be healthy without good nutrition, can you?), and transport, and just about anything else — that's exactly, how the above-mentioned metric goes up, yes.