In fact, I'd go as far as to say that, at current ride rates, Uber/Lyft would be able to replace/refurbish autonomous cars on an annual basis. Of course, rates will fall with autonomous cars, but not below the cost of depreciation.
Expanding the fleet to a new city now means buying land, building facilities, hiring mechanics and admin staff, and buying the cars. At this point Uber would look more like UPS - with UPS-like growth - than a tech company. All the while, unless they raise prices significantly, they're still losing money.
The cost of infrastructure and automechanics, etc, is spread across the fleet. That's the benefit of operating at scale - economies of scale. You don't lose money merely because you're operating at scale, that's not how it works. What would it cost you to maintain a Prius? How about 100 identical Priuses? It's not 100x.
Finally, the comparison to FedEx/UPS is flawed. Those guys don't just have a fleet of trucks to maintain, they have to deal with shipping centers, hubs, air transportation, multi-day package tracking, and the logistics nightmare that's involved in doing all that and still getting packages delivered. They'd rightfully tell you managing their fleet is the least of their concerns.
Car rental companies buy in sufficient bulk to get discounts deep enough that they sell at a profit in good markets.
Fleet maintenance and self-insurance is an issue, to be sure, but it's not the same as Fedex or UPS.
Uber already owns thousands of cars in Singapore.
Not a lot of VCs jumping into Fedex or UPS type businesses when you actually have to invest in a transportation network. Tesla Network might pull it off with their customers footing the capital costs (instead of Tesla needing to go into the markets to scoop up another few billion dollars in credit lines).