I disagree. Of course demand will go down as prices go up. It's quite literally the most basic principle of economics. Uber is not like a life saving pharmaceutical that people will pay any amount for - that is, an inelastic service. Consumers will absolutely avoid a service because it costs too much. Uber is no different. While people may still take Ubers, they'll take them less often. So Uber will still have reduced revenue.
> I couldn't convince the driver to give me a flat rate or quote to my destination
I'm from NYC, so granted our taxi fleet was well established well before Uber. One law established is a fixed cost to and from airports for cabs. Certainly this can be be replicated but yes, it's not something that can be immediately addressed and so Uber wins in this space (an upfront price).
To respond to your general message, yes, Uber is excellent in certain circumstances. This is one of them. Though I've also seen the reverse when traveling. Hoards of people waiting for an Uber, and plenty of taxis around.
As it currently stands, with prices going up, drivers' compensation going down, and Uber burning money, it's not likely sustainable. So Uber's future is at risk regardless of anyone's individual consumption
So, I got in the taxi thinking it would be around 60EUR (what an Uber usually costs). The taxi cost me over 100EUR to get home in 30 mins vs. 1 hour. I should have gotten an Uber but I was too exhausted to think of it and figured a regular taxi would be in the ballpark of an Uber.
Uber can give me a price before I even request a car. No taxi can do that atm and I don't think demand would go down because prices are increased.
If I knew it would have cost me 100EUR+ to be home in 30 minutes after spending all day in airports and planes, would I still have paid that much? I probably would've hesitated, but I think I'd still have pushed the button.