I think we're doing a lot of work to get into the mind of cab companies, but along those lines: they weren't interested because the market isn't really that large. Uber is barely profitable now after raising rates tremendously and aggressively fighting any kinds of workers rights initiative. That means two things. First, people don't think a typical ride is worth very much, and second, people don't really have that many places to go. The destination list is 90% work, the airport, and nightlife. These are not the underpinnings of a multibillion dollar business... unless you invent self-driving cars or achieve a good old fashioned monopoly (a lot of the reason many cab companies went out of business as you say is that Uber failed to invent self-driving cars).
But overall this was pretty bad investment for humanity. Let's just stipulate it's a lot easier to get a ride at a reasonable price and that's a good thing (not a given considering increased traffic and greenhouse gas emissions, plus decreased pressure for cities to move away from car-dependency). Was it worth multiple billions of dollars and software engineering hours? Like, assuredly not. It's a big "LOL" drawn in lipstick on a portrait of the efficient market hypothesis. It turns out the private sector is also great at just setting huge piles of cash on fire.