Restore Swipe to open (sort of)
I've found a way to almost restore the old "Swipe to unlock" behavior in iOS 10. The trick is to select an app you often use and add its widget to the widget screen (swipe right from home screen). Mail, Calendar, Safari, or a weather app may be good choices. Alternatively you can add Siri App Suggestions, which gives you a mini chooser of recent apps. Then, when you see the lock screen, swipe right to see the widgets, and tap on one. That will bring up the passcode screen, then take you to the app. When you're done with the app, you still must click Home to return to the home screen. So this doesn't eliminate clicking on Home, it just lets you do something useful on the way.
Note that you can now freely arrange the widgets by dragging the three-bar icons on the edit screen. You're no longer constrained to Apple widgets on the left, others on the right. But nothing you can do about that doggone clock...
iPad Air, iOS 10