In old versions of the iOS App Store, every time you downloaded a new app it would close the App Store and navigate to the screen with the now-downloading app. Recent versions of the App Store keep it open and force you explicitly exit. I’m surprised that the App Store didn’t launch with the new behavior - it must have been a conscious decision since the development effort for both seems similar.
The only time the original approach is faster is when users intend to download a single app. I suspect this is actually the most common scenario and someone at Apple decided to design the App Store to optimize for it. Unfortunately, they didn’t consider the frustration of having to download multiple apps - even if one only does this a fraction of the time. Training yourself to hit the home button after downloading a new app is a lot easier than training yourself to scroll to the App Store icon, clicking on it, and resuming the app search. Even if 90% of the time a user is only downloading a single app, the other 10% matters is significant given a large enough cost. One can forgive Apple for launching the iPhone with this behavior - no one knew how people would use the App Store. But why did it take years to release the update?