A TD isn't needed to win. The way I remember reading it was that it reverts to the old "sudden death" format after the first two possessions like this:

Team A gets ball and scores TD it's over.

Team A gets ball scores FG, then team B gets a chance. Team B scores a TD on that chance it's over. If Team B scores a FG, then it becomes sudden death i.e next score (FG or TD or safety) by either team wins.

So it won't be that both teams keep kicking FGs.

This is how i remember reading it anyway.

You forgot this scenario:
Team A wins the toss. Team A punts on first possesion.
Team B kicks field goal on their first possesion...
Game over. Team B wins.

True. I also forgot:

Team A wins the toss and gets the ball. Team B safties them on that possession. Game over.

and:

Team A wins toss. Team B onsides kicks and recovers. Team B kicks FG. Game over.

And
Team A wins toss and gets ball. Team B pick 6. Game over.

Boy, that would suck. Lose a playoff game in overtime by a safety.

It would. Do you think it is worse than loosing by giving up a TD on the opening kickoff?

At least this way you wouldn't have to worry about missing your plane. LOL