Different people evaluate & value those three differently. To get a customer that equation needs to yield a higher value than the next best thing. To win in a a market completely, you need to tick all three boxes. Better, cheaper, faster.

Uber focused on high quality early on, the limo market. They beat limos for price and convenience (the competition sucked) and matched the quality. More expensive than taxis, but better quality (nicer car). As the network grew, "convenience" went up, fast pickup times. They expanded downmarket (lower price & quality) with uberXand to take on Taxis.

I think this ridesharing/carpooling, if it works well might find an unserved niche somewhere between Taxis and public transport.

A next step might be something close to public transport. Basically minibuses running something similar to shuttles between hotels and airports. Most cities have these. They are possible because hotels can coordinate. That's why they are more common between the hotel and the airport than the other way around. There are probably lots of other use cases that are just missing the coordination.