Not just saying this cuz the Pats won in OT. I've long thought the rule pretty stupid.
To me, the most logical and fairest way to set things up is this:
Add another timed period, like they do in college basketball (with some tweaks). The team ahead as time expires wins. If they're still tied, go to one more timed period. If that fails, game is a tie. This takes away the aspect of the luck of the coin flip, adds more drama, forces both teams to be strategic and manage time and timeouts, etc. etc.
Not sure the best number of minutes to set for the OT period. Perhaps five. Maybe ten. But I think that's a much better way to do it than the first TD scored wins.