#2. Only a select number of superstars were allowed
Vince McMahon came up with the plan to allow three superstars to be part of an invasion of each brand in the coming months, which he calls the "Wild Card Rule." The fact that Xavier Woods wasn't with him on Raw could have literally just been because McMahon wanted it to just be three superstars, something that he later changed to four because he was scared about Lars Sullivan.
The most Woods would have done on Raw was hang out at ringside and perhaps talk for Kingston at the beginning of the show, which was stuff that wasn't needed since the WWE Champion was able to talk for himself and go on to set up a fantastic match between himself and Daniel Bryan which went on to become the main event of the night.