Why doesn't the "market" sort this problem out.

Essentially these companies "own" connecting supply and demand, but I fail to see how that prevents competition from forming and providing a better alternative for both?

Right now, as a demand user of Uber, I like that the company is very protective of my experience, something that is painstakingly difficult with traditional taxi services. But if Lyft offered me the same experience or better, my switching cost is nil.