Screen waking after pressing the power button isn't instantaneous
On my SHIFT6mq it takes a good 2 seconds for the lockscreen to come up. It seems to be quicker when I shut off the screen when the lockscreen is already open, so I'm guessing the delay comes mostly from the fact that the lockscreen needs to be started and it's a slow process. That is also evident because from a unlocked phone to a locked one and then turning the screen on makes the lockscreen not show the background for a second or so (but other elements are shown) which is not the case when coming from a locked phone with screen on to screen off to screen on again.
I'm guessing the screenlocker needs to be loaded into memory either quicker or when the screen is still off.