I agree that the problem exists, but I still don't like your idea. There is no need to build such redundant artificial restrictions, especially since we have overcome so many of them after Jonne had noticeably extended the scriptwise part of the gamemode. So, -1.
In turn, I suggest to fix a little bug. Right now, securities lose their spawn protection if the President stays on the spawn for more than a minute; same happens with cops if he drives past their spawn. But the freshly spawned cops or securities still have their spawn protection, even if the president is there; it causes chaos and no spawnkilling textboxes randomly popping out for the terrorists, and it should be fixed.