5v5v5

Except League of Legends was not balanced around a three-team siege.

Starcraft, and other RTS games, allow you to micro-manage massive armies, scout out your opponents, and plan encounters all on your own. You are your team. Now, sure, you can agree to team up with another player, but that's balanced out by the fact that a single player--doing it right--can actually become a threat to multiple players on their own.

League of Legends doesn't have 1v5-level scaling.

While DotA does, and could probably handle a multi-team game of Cutthroat, LoL runs into the problem of scaling ending much earlier, meaning the playing field can level much faster. You can't get a champion to level 25 and proceed to 1v5 a team, and pull off a win thanks to a 9-second immunity to spells. You can, at best, be five levels ahead of your opponents and maybe pull off a 1v3 against people who are even slightly coordinated.

Your team can't massively out-scale another team, because scaling limits are much harsher in League of Legends than in Starcraft. So you'd eventually run into the problem of each team trying to figure out how they're going to destroy the other two teams. Either two teams bum-rush the weakest team to end them as fast as possible, or all three teams end up turtling worse than Season 1 tanks.