If they are so important, why don't they need an executive key?
Aboard a starship, that is not necessary. We are all capable of exercising self-discipline.
StarFleet Security measures: Anyone who is not a member of Starfleet or the Federation can just go anywhere and use anything.
Seriously, these people are onboard a ship that can identify you by name, rank and locate you anywhere onboard, and at no point does anyone tell the computer to limit their access. It's even more silly when you realize that a couple of episodes ago, an escaped Klingon prisoner was able to make his way to Engineering and threaten to blow up the entire ship by shooting at the warp core. If it's so easy to destroy the ship, and every crew member onboard has a high rating of self-discipline, why does it take two senior officers to activate the self-destruct sequence? It's kind of like that Simpsons episode where Mr. Burns and Smithers go through a lot of rigorous security measures to get into the room the controls Springfield's power, even though the same room can be accessed outside via a broken screen door.