Why wouldn't they rig it? Is not like there is some kind of special reward for the winning team or anything, so rigging it its "harmless" on the grand scheme of things. But for lore purposes? It could add something cool to the story, like what OP suggested for instance, hunters dont have a boss right now, having a big ceremony announcing the victors AND a new vanguard would be cool, especially one that could cause discord among the tower, is pure lore juice waiting to be squeezed.

Look for instance warframe, they have an small event that if the community fails a player hub (something like the tower) gets destroyed, the 1st time it happened it was rigged so that we failed, because it was planned for half of our relays (what we call the player hub) get destroyed, now the event happens from time to time and is rigged so the community never fails and nothing destroyed, all for the sake of lore.