There's a lot of companies and cooperatives from a quick look. Even cities rolling their own. Uber/Lyft is handing an entire market over to a lucky competitor,
Uber and Lyft combined have raised upwards of $20 billion in venture funding and have been operating unprofitably for the last decade and a half. There's a reason the "free market" cannot simply replace them in a day.
This is a really elementary misunderstanding of free market principles. That theory only holds if the market is actually free.
As an extreme example, if they regulated minimum $1000 per ride. No logical person, free market oriented or not, would expect "alternatives" to take their place.