My SP3 exhibits the same behavior. When I open the cover the keyboard cover backlight turns on but the display does not. If I hit a key on the keyboard, the Windows softkey, or the power button the display will turn on immediately. This is different behavior than my SP2 which turned on the display when the keyboard cover was opened. To be honest I'm not sure this is a bad thing. I had several instances in the past with my SP2 where I found it powered up in my backpack. I always assumed that this was due to the keyboard cover moving slightly while I was on the move.
(moderator edit: I have split this post into its own thread as the behavior is different than the OP had posted about)