During the initial 60 minutes there's the strategy of clock management. Do we let the other team score so we can save time and get the ball back, giving our offense a chance to win the game? Do we burn our timeouts on defense to save the clock and hope to hold them to a 3-and-out or preserve them for our final offensive drive? Do we run to the sidelines getting little chunks of yards to save the clock or risk a pass downfield, risking a timeout being burned? Do we take an intentional safety so we can pin them further back on the kickoff instead of punting it?
In overtime the game clock doesn't exist (except for the regular season), which is why your analogy doesn't work. Overtime is basically a brand new, 0-0 game and the first team to score wins. That's why it's dumb. We'll just pretend we spent the past three hours doing nothing and whoever kicks a FG first is the winner! For teams that have scratched, clawed and bled just to make the playoffs...I can't even imagine what'd it would be like to barely let a team across mid-field and have their kicker drill a 50+ yarder and then be told you have to go home. Back in the day it was a fine format but with all of the skill in today's game it's just too antiquated.