If the Titor story was true then what we know as John's (the Johns') mission is the limit of an infinite number of missions and the motives of the successful mission wouldn't be John's. They would be the motives that survive to infinity. Those motives could overlap but the critical consideration is what survives to infinity, not what he wanted to do. All of the time travel missions that ever happened all combined to produce to missions we now refer to as John's. Also, perhaps the people on those timelines had to go back and change our timeline because of the events that unfolded after DARPA was the first agency to develop the application. Perhaps they were not the first ones on our timeline and that rebalancing of the power and initiative leads to a timeline that isn't so horrible that people decide it's better to go back and change history than to just deal with it. Whatever the mission is or was, and whomever was the mastermind behind it, the likely goal was to produce a timeline that was good enough so that the people at the end don't feel like they they have to go back and alter it.