Why can't we have ties? Why can't a game end with each team having the same score? Why must there be a winner and a loser? And aren't some ties in fact really good games?
The National Hockey League has held for several seasons now 'shootouts' to break ties. Soccer has had championship matches decided in like fashion. If there's a dumber way to break a tie I cannot imagine what it is. Such a process cheapens, indeed I would argue that it mocks, a victory anyhow. Winning on luck is nothing to be proud about.
There is fear, now that the National Football League has cut overtime periods to 10 minutes, there will be more ties in football this coming season. But so what? If teams played to a draw, it's a draw. Let it stand.
Even in championship games, why can't there be co-champions if the result is a tie? They're only games after all; entertainments; diversions. They aren't really that important.
Let ties stand. If it buggers your standings or your ratings, or especially if it buggers your demand that someone must win and someone else lose, I don't think you're particularly sportsmanlike at all.