But is that true for most people who use Uber, or even taxis? I wouldn't be surprised if a large portion of Uber/taxi users were in fact people traveling to a different city.
I would be surprised. At least in New York, people use taxis very often, and thus use Uber very often. I'd wager the vast majority of Uber usage is in people's home towns/cities.
Personally, I use other apps when in NYC, but fall back to Uber when I'm somewhere else and can't find a local app.
This is exactly what got me to use Uber initially. I can show up in San Francisco, or London, or my tiny hometown where cabs take 45 minutes to arrive, and Uber will work the same way for about the same price. Having a robust, universal way of getting places really does matter to a lot of people.
Where I grew up, the vast majority of people I knew very rarely left the county they lived in - even though it was only a couple of hours to New York, Philadelphia, Baltimore, Washington DC. By the time I moved to Philadelphia, my social circle was much more likely to travel - but on the whole, the greater population of the city tends to stay within the city ("I have everything I need here, why would I bother with the hassle of going somewhere else?")
Hm, ok. We'll here in Europe things are a bit different. Most people travel, it is pretty easy to do so and even the 'poor' (students, people that only have bikes) move from city to city regularly.
I've got acquaintances from all over the planet though, and even there most people travel with some regularity to other cities. Holidays, family visits and so on, and then of course there is business travel which I would assume is one of the larger customer groups for Uber/taxis.
Most people only go to another city once or twice a year, so it's not a significant issue for them.