Hedge funds don’t have as high of institutional ownership as you assume. It’s actually pretty small.
That said, nothing about the situation you described is at odds with “free market”. You’re describing the operation of a free market.
I think a lot of people want “free market” to mean the opposite: A highly restricted market where they are protected from any supply and demand inputs from anyone else. They just want cheap things and don’t want to compete with anyone.
There are two sides to a free market, though. In your example where a hedge fund comes in and buys your entire neighborhood, they would have to do so by outbidding everyone. This drives up the price. If it’s an economically irrational move you’d be smart to sell your house to them at an inflated rate, too! Then move back in when the prices crash down.