Fundamentally, I think this is because professional sports are entertainment. People have paid for nine innings of entertainment; cancelling several innings of that entertainment because one team is getting routed would deprive the fans of the other team - the routing team - of several innings that they might be finding highly entertaining. That's entertainment they've paid for. There's also the little matter of paid advertising - and cancelling the last three innings means cancelling a bunch of paid-for advertising minutes.
In Little League and such amateur settings, the games are (or at least should be, helicopter parents notwithstanding) about the participants - they are athletic competitions for their own sake, for the sake of the players (for their egos, or for their development of character, etc.). But professional games aren't about the players; they're about the paying fans (whether in the park, or watching on paid-for television broadcasts), about keeping the flow of money coming, about keeping eyes on the paid-for advertising.
Moreover – always remember "If we lose this game, I'm walking home." Ridiculous comebacks happen... and they're very entertaining, and very memorable.