I believe it would be disastrous for the game. If you eliminate kickoffs, then you've also eliminated onside kicks.
Without onside kicks, you are draining the drama out of a huge % of your close games.
Plus, it seems a little silly to get rid of the onside kick but maintain punting. Maybe the evidence says that the punt is a less injury prone play than the kickoff, but I would have to see the data to believe it.
In any case, does anybody know of a petition to keep the kickoff? And if not I think we should start one and pass it around all the major SB Nation blogs, Rivals, Scout, and 247 recruiting sites, etc.
Could take some grass roots activism to keep the kickoff.
Finally, if concussions are such a danger, then have teams kickoff from the 38 or the 40. That would drastically increase the # of touchbacks, thus eliminating a lot of potential injuries.