The problem is not only objectivity; it is a lack of information. If everybody played round robin, I agree that the computers could run a matrix and determine who performed the best. However, this doesn't happen in a 12 game football season.
It is impossible to quantify a night game in a hostile stadium, or a team that has improved throughout the season, or a game that turned on a bad call or a bad bounce, through purely statistical methods. This requires subjectivity, which is something the computers are wholly unable to produce (and are specifically designed not to produce.) Take a quick look at the "Billingsley National Champions" if you need some examples--they crowned Miami in '90, Penn St. in '86, Florida in '84, Oklahoma in '80, USC in '76, and they are far from the worst (that honor probably belongs to FACT or Sagarin.)
The human polls, of course, also have their flaws, as they do often lack objectivity. The BCS has tried to overcome these shortcomings by combining the two, but the fact is there is no perfect system.