For most purchases, people really only have vanishingly few choices of companies to buy from. A truly free market might work, but the profit motives that have corrupted our political, legal and regulatory systems has made most markets into oligopolies. These companies work together to manipulate prices, without ever directly communicating in a way that can be punished.
For a free market to really drive prices down there needs to be real competition. When eggs went up in price, they allegedly did so because of avian flu. But that flu only affected a small amount of the production. Cal-Maine, the largest egg producer in the country, lost no egg production at all. Yet they increased their prices massively. If the market was working as you say it does, Cal-Maine would have kept their prices low to capture more market share. Instead they saw that other producer might have to raise prices and preemptively raised their prices.