What you said doesn't make much sense. Much more important than the algorithm is the market that the algorithm operates in. Uber couldn't unleash a magical algorithm and solve commuting inefficiencies for every user if there isn't a sufficient density of both riders and drivers (i.e. the main inputs to the algorithm in this case).
That doesn't seem to be a problem for the competition. Prices are the problem, and Uber is trying really hard to lower the prices and profit, that's why the algorithm IS most important.
I really do not understand why almost everyone thinks that "network effect" is the best thing Uber has, when it obviously isn't.
It is. I get an uber where I live within 2-3 minutes. And sometimes I've gotten uberPool matches essentially going to the same destination picked up within a block. These are only achievable with considerable penetration into a local market.
