The same can't be said for public transit, except for trips that happen to follow a major train line.
So I purchased a nice toyota for about $15,000 about 4 years back. 600 miles per month, 25 mpg, about $100 on gas every month, about $1200 every year. Assuming that I use this car for another year, I paid out $3000 for every year + $1200 on gas=$4200 /year (I'm sure my car will last far more than 5 years). Uber is about a dollar per mile. So every month I would have to pay $600, every year about $7200. You could try and hook me up with another person traveling the exact same route, but that is going to be a very uncertain thing even if you have the relevant technology. Even a small degree of uncertainty will lead me to buy a car.
Now if I used public transport, I would pay less than $1000/year. Plus, there wouldn't be much uncertainty. I think the world would be a much more efficient place if we tried to make the $1000 ride more convenient/efficient, than if we tried to bring down the cost of a $7200 ride (although I hope they can do it, would love to see how they do it).
I never said ride sharing is all doom and gloom, I'm just saying it will have a smaller space in terms of number of people traveling.
Was Uber designed to be the cheapest form of transport? I doubt it. You have pure convenience on one end (car ownership) and pure cost saving on the other (public transport) on the other. The taxi system lies in the middle, so does Uber. Taxis will have a space in the transportation market, just not the biggest space. I might be wrong here!!