Because, playing off of the original advertising campaign, their slogan is "There's a soldier in all of us" and so they picked him because he's such an ordinary-everybody type. The sort of person who works hard doing some job that may not be the most rewarding or exciting, and gets to come home and pretend to be something badass via gaming. Not everyone in the commercial, however, is the ordinary-type, there are some wealthy sorts and celebs, enforcing that even people not in "ordinary" life mode, living what most would consider exciting and/or unusual lives, need a little make-believe escape also.
They could have probably picked any character from the commercial, but they probably picked Burger Man because the fans liked him the most. Call of Duty's developers have always been eerily fan responsive. There have been times we'd be playing and saying "_______ would be awesome to put on a map" or "Imagine if they ever put ________ in Nazi Zombies.." and then the NEXT map pack would be released with many of the things we'd discussed implemented. I think they listen to us on the mics ...conspiracy!