To get as big as Uber means they need to be as convenient which means that there's
always a car available. Uber handles that by being multi-brand, and by incentivizing their fleet with surge pricing.
Toyota would have to prepare for worst-case load and let those cars sit idle to keep them available. And they'd have to do that in almost every city in the world or their app would just be another local annoyance.
Also, if you order a Toyota and a Ford shows up you're going to laugh and tweet it.
On the other hand, it does give them a stable production target which would level out manufacturing spikes...