Well, that IS essentially what they did. They went to the Board, and from that, picked someone from it they felt comfortable with. The guys on the board are there to do exactly what Accorsi is doing right now - that's their jobs.
Its been done before this way as well - in I think it was 2012, the Panthers picked Accorsi, and look where they are at now, with the talent and getting past the 1st round in the playoffs - their GM was an Accorsi-approved guy.
Ballard really isn't any different. People make a big deal over his Bears tenure, but from what has been said by non-Bears people after Chris's name was first leaked, you are hard pressed to find any negative criticism at all. The only one I could find was Hub Arkush, the same guy who got mad that Emery reached for Kyle Long, arguably Emery's best draft pick in his tenure - Hub is a slave to his connections and far from objective as a result.