For the screenshot thing you have to be inside an app. Take the screen and after tapping on "save to gallery" try to exit the app. It won't let you except after 1-2 seconds. What a disaster.I tried both of the things you mentioned - 1. saving a screenshot and then immediately swiping up and 2. opening a link in Safari in a new tab and immediately trying to scroll the page I'm on.
Number 1 is immediate and very responsive, when I swipe up I am on the home screen immediately.
However, number 2 isn't responsive and I have the same result you do, I swipe furiously on the screen until the animation is done and only after a second (or more) it registers the input and I can actually scroll the page.