That's not really true. Uber/Lyft have almost always been marginally profitable. Meaning they charge more for a ride than they pay the driver to perform it. Their massive losses mostly come from ridiculous overhead plus marketing to grow the business.

On the other hand, the taxi market never really worked because there's no price fluctuation to mediate supply and demand.

On one side you have places like Dallas, Atlanta, Phoenix, and others where taxis basically didn't exist for locals. On the other you had places like NYC where demand often outstripped supply. You wouldn't be able to find a cab or they wouldn't take you where you wanted to go.

You can also see it in medallion prices. They were so profitable in places like NYC people were paying a million plus simply for the opportunity to operate a cab. An obviously broken market.