But why does it need to be? I would still take a Lyft/Uber because the service is better, even at the same price.

You’re probably atypical. I don’t use any of these services much and am not very price sensitive especially given that it’s almost exclusively for business travel. But I’m guessing a lot of people using these services care a lot about 2x differences in price.

It needs to be because they're the new(er) player. There's a vast difference in attracting customers between "costs the same, but it's neater" and "it's neater and cheaper!".

Once all the full-time taxi drivers are out of their traditional cab job, who do you think they will drive for?