I believe you are onto something there. What did people do before Lyft/Uber? They walked more. They biked. They took public transportation. Maybe they drove themselves. Maybe they drove/carpooled with a friend. Maybe they took a good old fashioned taxi.
Faced with a price hike attempt, those options are again always on the table.
But I feel like the Lyft/Uber mode of transport is generally more spontaneously and is therefore generally more elastic. Sure, there are undoubtedly some inelastic use cases, like regular commutes, but there are also some very elastic use cases, like a ride home from the bar or a rescue from the rain. I am definitely interested to see how the breakdown of these different use cases turns out to be, but for me and my friends and peers in the SF Bay Area, the latter use case definitely dominates.
However, my sense is that for at least certain locations/demographics, that's probably changed with Uber/Lyft. I don't personally use them much but anecdotally a lot of people have started using them as an alternative to public transit or just because it's easier if they're going out for a night on the town. And I work with a lot of people for whom the reflex seems to be to pull out a smartphone anytime they need to go more than a few blocks while traveling. I expect those behaviors would change if the price suddenly went to 2X. (It also definitely makes a difference at the margins when renting cars and that's mostly a straightforward price calculation.)
They manage demand via surge pricing, I thought. So is it really elastic?
The basic economics of Uber/Lyft-style transportation is very profitable. The biggest economic challenges are 1) entering a market and 2) pools. And Lyft & Uber fighting each other.
The drivers gladly use multiple apps so these businesses don't really hold much power in terms of lock-in.
1. Start in one city only and concentrate on that. 2. Get your service listed in Google Maps. 3. Gradually expand.
Job done. The only real defence against that is that Uber/Lyft could probably afford to undercut you until you go out of business, Walmart-style.
I don't think there are many people who doubt that ride hailing apps can be done profitably. I think the big question is (a) is it a commodity business (I personally believe it is) and (b) can potential profit margins support their astronomical valuations.
I think the main problem (though MUCH more so for Uber than for Lyft) is that it is valued as a "network effects" business, e.g. something like a Facebook or a Google with substantial pricing power, but I think the reality is that it will turn out to be much more like the airline business - basically a commodity business where raising prices is extremely difficult.