Neither Uber nor Lyft are going to go bankrupt. They lose money intentionally as part of their business plan, which at least for Uber, is around growth and cornering the market or becoming the "go to" service for the things they offer. Their quarterly losses are not unexpected, they're planned for.
Still, as a hypothetical question, I think if Uber and Lyft go out of business, they have shown that technology can be used effectively in the taxi industry to make more rider-friendly taxi experiences. Pre-Uber, taking a cab in my city was annoying, with a dispatcher phone line that was *Always* busy, a rude dispatcher who routinely hung up on you, and a solid chance that your driver would never show up or your driver would show up, not see you, drive off, and then you'd be stranded. The cabbies didn't reliably take credit cards (this was like... 2010s too; At least once a cab driver refused my card mid-trip, and wouldn't take me home unless I went to an ATM and took out cash, and he kept the meter running the whole time) and it wasn't a safer experience than any time I've taken an Uber for me... with enough experiences where the passengers and I openly wondered whether cabbies were drunk or on drugs. Then, of course, was the notoriously racist drivers and/or dispatchers, who would ignore dangerous neighborhoods or say they're all booked up and it'll be an hour+ if you need a ride home from a poorer part of town. But they were literally the only game in town, you had nothing else. Uber came around and changed everything, and changed everything in a matter of months, while the cab industry here was so stubborn because they had no incentive to change.
Now where I live there's more car services available, and the cab companies have had to join up with app networks so you can book rides from your phone and watch your driver coming to hour location. For years, the cab industry had a monopoly on the city that didn't get broken until Uber and Lyft came around and proved you could break it. It was a government sponsored monopoly, backed by organized crime, that pretended that any advancements to technology or the rider experience -- even simple things like accepting credit cards -- was just impossible. There would be no uber and lyft today if the cab industries didn't woefully under-serve customers for decades with a protected monopoly.
