I didn't notice this before, but I let my screen timeout and you are right...the app which was open disappears. But I've found, by doing this several times that it's inconsistent. Sometimes the app will be open when using the home button, other times it won't. What's even more annoying is that if the app was opened from a folder, the folder does remain open, but not the app. I too would prefer the home button, rather than the power button, allow me to pick up where I left off consistently. I find it a bit difficult to use that side button anyway because of the case protector on my phone.
Other IssuesAnother issue I'm noticing since the update is horrible scrolling. I thought there was supposed to be improvements to make scrolling smoother. My home screens jerk and when on an app, there is such a disconnect between what my finger is doing and what the phone actually picks up. It's really a pain.
I've also noticed random times where I open up an app and just kicked out of it. It just closes by itself for no reason.