I haven't heard of any Icon that doesn't have this delay, or doesn't need multiple clicks to be awaken. I'd say less than 10% of the time it wakes up instantly.
Mine wakes right up with only one click of the button, also the only time I had a problem with it being "busy" and having a delay when waking back up was when I had live lock screen beta installed. Then after I uninstalled that I thought it would go right back to normal, but the delay was worse, however I can't remember but the fix was posted on the discussion for that app on this site. I really can't remember but all you had to do was set one of the preinstalled apps to their default settings. I will look for that when I get to a real computer, right now I'm on the road.
But again right now i have absolutely no problems and there is no delay or no multiple clicks to wake my phone. Right before i installed the DP version of 8.1 i was having a problem with my contacts sync'ing with the VZW back up assistance server, and the Tech i was talking with had me do a hard reset, so right after that the first thing i did after hanging up with her was installed the developer preview. And all had been good...