Have there actually been studies that prove Uber is significantly cheaper than cab?
Anecdotally speaking, I've taken Uber quite often in Austin, as well as various cabs, and they always seemed comparable to me. In fact, if you take into account Uber's surge pricing (which cabs don't have, afaik), Uber came out more expensive on average.
In Lisbon, it's mixed, since the price per minute is lower (0.10€ vs 0.25€) but the price per km is higher (0.65€ vs 0.47€). Taxis have an higher base fare (3.25€ vs 1€) but on the other hand the first 2 km are free.
Anecdotally speaking, I've taken Uber quite often in Austin, as well as various cabs, and they always seemed comparable to me. In fact, if you take into account Uber's surge pricing (which cabs don't have, afaik), Uber came out more expensive on average.