I have tried and tried to replicate this home button delay. It is simply not there however many ways I try it. I tried to replicate issue on an iPhone 6 (16 GB) on iOS 11.0.3, an iPhone 7 Plus on iOS 11.1 Beta 5 and on a 5th Gen iPad also on iOS 11.1 Beta 5. Once the home button is pressed from within an app, the animation starts immediately and is smooth and fluid. Sorry but I do not see the issue. And don't say I don't possess the sensitivity to see as I am one those very sensitive and observant people that pick up on minute details most don't see.
All of those configurations should behave the same. You need an iPhone 7 running iOS 10. And the animations are smooth I agree.
Does anyone remember on iOS 10 with a iPhone 7 that when going into the app switcher. The opened app used to jerk down before jumping to the side? This doesn’t happen anymore as they have added a small pause so the app doesn’t immediately shrink upon pressing the home button before going into the app switcher.
This is probably one of the reasons of the delay. Instead of revamping the entire animation going into the app switcher they increased the wait for a second press.