One theory:
The original game of football (read: rugby) was super grindy. It was like taking two Greek phalanxes, say the Spartans and Athenians, having them lock up front line to front line, shields against shields, and just start pushing at each other. Game of inches. Meanwhile, you know, all the stabbing between the shields is going on causing attrition until one side starts to give way. Brutally slow, dusty, and unforgiving way to fight.
And that's how football felt in its early days. I mean, this ancient idea of warfare is kind of WHY football (rugby) felt that way back then. Football as a war game, indeed.
So how do you break a tie when games might easily--in fact, often did--end up 0-0 or 3-3 or 7-7 (or scores that would sound weirder today, because goals and field goals had different point assignments back then)?
If the essence of the sport is grinding two formations against each other in an effort to slowly gain ground ... what could you possibly put in as a tie breaker that wouldn't violate its nature? Lining up at the 2-yard-line and giving the offense a certain number of seconds or plays to get across the goal? Well that would be no good, because those teams just spent 60 minutes proving that neither could push the other back any distance at all! How about allowing each side a free kick, a field goal attempt? Well, that's not the spirit of the game. Might as well let the team captains play a round of checkers to break the tie, as much as either represents the sport.
So, since there was no conceivable tie breaker that stayed within the framework and essence of the game, the football world accepted that some games just ended in ties. Shrugged and got on with life.
Then football evolved, became more friendly to the offense. The forward pass came into existence. Later, it actually became popular.
But even then, for a long time, the spirit of the game as it was originally lived on in the minds of the coaches and referees and officials. And tradition also had taken root. Tradition is a big part of sport. And so even after we had the means to break ties while staying inside the 'feel of the game,' we still didn't take advantage of the opportunity for a while.
Then, finally, we did.
But that, i think, is why for so long we didn't.
Go Vols!