Earlier quoted context omitted.
Would you want to download a different app every time you traveled to a new country? If you're in the EU/APAC with many countries close together and travel for business? Uber works relatively well in every country you go to, including at one point, China. Not many apps have ever accomplished that.
I wouldn’t mind if the app started up and said, “download the $country_or_region extension,” but that is just me (assuming it doesn’t require re-creating an account, or re-entering billing details).
Uber made the right choice.