Platforms win out because of user familiarity, not because they're necessarily the cheapest option.

Uber had and still has a large lead on Lyft. They get free advertising all of the time through the media. How difficult is it to accept that you're not going to be number one in every market (but you'll likely remain number one in most markets), spend money wisely to shore up your position when necessary, and do everything you can to stay profitable?

The barrier to entry in ride sharing business is so low it's almost non-existent, which makes the whole strategy pointless, unless they can lobby in Congress for some regulatory framework that would make starting a new ride-sharing business harder.