What the game needs -- has always needed since the very first day of CoV -- is PvP missions, where a team from each side queues up and enters an instance, just like a normal mission, except the two teams have competing goals. One team want to power up the doomsday device, but the other team wants to destroy it. One team wants to steal the goodies, while the other team wants to protect them until backup arrives. One team wants to break into a facility, while the other team wants to find and arrest the intruders before they can get in.
Apart from the PvP framework of the mission itself, all of these objectives are easily doable within the scope of existing mission design. Queueing up could be handled through the LFG interface. I've never understood why this never became a thing -- it just seems like such an obvious setup to me. Yes, it requires a bit of cooperation to get two opposing teams together, but so do raids and TFs and costume contests. I'm sure the players can handle it.