Uber gains benefit of functioning better under low/no connectivity, better location access and local/remote notifications as well as visual integration (e.g. showing ETAs and updates in the Dynamic Island or on the Lock Screen).

Some of these (increased caching and remote notifications) you can get on iOS if you install a web app as a Home Screen icon, but as just a website Uber might not get their minimum bar of functionality for widespread use. So far, I haven't seen any large companies have installed web apps as their go-to-market strategy.