I was thinking, why isn't 3-flag in Big Team Battle? I've played it a few times on Asylum and Zealot. Its fun, but with those small maps, it tends to get way too chaotic to understand what's happening.
That same gametype would fit perfectly on a 8v8 map like Hemorrhage or Highlands. Multiflag in BTB usually requires either a stealthy-but-lucky approach, or pushing the enemy back to the point where they are being spawn killed just to capture the flag.
This is just my opinion, but one of the reasons BTB flag isn't as fun as it used to be is the ease at which players are able to defend/camp their bases. Hemorrhage gives almost no reward to players that control the middle of the canyon, plus there is a Shotgun right next to their base. Highlands has more incentive to controlling the middle, but it's still easy to take a sniper and rocket and hold your own base. Having a neutral objective will actually force players to move from their base and fight to control parts of the map.
On top of that, having a neutral objective would encourage players to funnel into certain areas of the map, while still trying to make sure no enemies slip by their defenses with a Warthog run. Imagine 8 players converging on the Plasma Launcher spawn on Hemo to fight over the neutral flag, while other Warthogs will try and make a run to the enemy base. You'd hardly have to worry about players camping in their base, since they will likely be out trying to fight over the middle ground instead.