Well, I actually like the fact that when the clock hits zero, you need to have more points than the other guy. I disagree that regular season games are decided "arbitrarily." You have 48 minutes to get more points than the other guy. If you're tied, you get another 5 minutes, and another 5... The teams aren't playing the clock during the game, they're playing the other team. If they're not ahead when the clock approaches zero, that means they didn't play as well as the other team did during the first 47 minutes and 30 seconds, and they deserve to lose if they can't produce on the last possession.

I also follow NHL hockey, which is also cursed with the concept of ties (and even gives a point for losses during overtime, a concept that boggles my mind.) I would prefer NHL games would have a 5 minute overtime followed by shootouts. Put your best scorers against their goalie and see who wants to win.

I guess it boils down to the fact that you're there to win, and in a tie, nobody wins. The objective of a game is to determine who the better team is, and no two teams are "evenly matched." Does the best team ALWAYS win? Nope. But not all ties are the result of two evenly-matched teams either, sometimes a team just gets lucky.

Incidentally, I like your decrementing team count idea, but I'd rather see the field made smaller and the games be 9 or 7 per side throughout the game. Having 11 people on a team makes it so difficult to score, no wonder there are so many "nil nil" ties.