A few months ago they changed their app so that iOS users no longer had the "only while using" option for location access, and announced plans to stalk users even after their rides had ended.
We could try to build a network to deliver applications, which would stop when you close them. We only need a system to map names to ips and some standards for protocols. We could even run them in a sandbox for security. Would be awesome.
It's not necessary to uninstall the app after each use to prevent tracking - in Settings...Privacy...Location Services, you can disable location on a per-app basis.
(this is admittedly a pain, and Apple enforcing in-use-only option availability is a welcome change)
That's what the "Only While Using" option is all about. In iOS 10 (and earlier), apps could choose to request location tracking "Only While Using" or to request it "Always". Uber switched from the former to the latter. And the article you're commenting on is all about how iOS 11 will add "Only While Using" back as an option for all apps, so you can set it that way even though Uber doesn't want you to.
It is not allowed for apps to refuse to run without location permissions. If you do that the app will be rejected. So no, 'usually' apps do not do that. iOS is not Android.