iPhone 5s: Have to wait before I swipe after unlock animation is done
This isn't a solution (I doubt there is one, at least without jailbreaking), but it seems you can open apps immediately. So I would recommend putting those apps that you want to be able to open right away every time you check your phone like email on the bottom, so that they are always there. 

It also looks like pressing the home button to swipe all the way left to the first home screen does not have a delay, so you could put apps on the first home screen and press the home button after unlocking (which is easy as you finger is already there). When I tested it it seemed pretty easy to accidentally activate Siri, so you might want to disable her if you do this if you don't use her.