You have probably never played the red/green game. What you are describing is how many people think people will act. That is *not* how people actually behave though. There is a very simple and common schoolroom exercise that illustrates this fact.
It does not matter to what degree political players may be acting in the pursuit of self preservation. They will act in ways that are counter to their own self preservation if they percieve a risk of others taking such action, or that their own lack of action will allow someone else to "pull ahead" of them.
Yes. But they will do it anyway, out of fear that someone else might succeed. I don't think you are fully grasping the massively greater motivation for people to "try to gain control of a gate" versus "work to prevent someone from doing that". People will always work much much harder for personal gain than they will merely to maintain a status quo.
We have no way of knowing how many hundreds or even thousands of evil groups did *not* try to take control of the gates over the last 50 years purely because they did not know they existed. I suspect they were made vastly safer by keeping them secret. Certainly, everything else remaining the same, they were safer by being hidden.
If your reasoning worked, then we would see methods like this used in real life to prevent any of a number of highly dangerous things from being used by crazy evil people. Not surprisingly, the methods actually used look a lot more like the ones the Scribbler's used, and not at all like what you are proposing.