The red book with its trigger words were kept in a single copy in a secure location, offered only to trusted personnel. Obviously Red HYDRA wouldn't want just anybody who could operate the cryochamber to be able to deploy the Winter Soldier.
Suppose that this was also because once the words were spoken and the Asset recognized a handler and received a mission, they couldn't be over-ruled except by hitting the Asset very hard in the head.
Steve & Co. (or for extra trust issues, Tony & Co.) for some reason have to thaw Bucky out and take him on a mission or flee. The enemy has Bucky's code words and a bullhorn.
The only way to keep Bucky out of enemy hands is to say the code words and give him a mission before the enemy does.
In Case of Emergency, Use Words
Suppose that this was also because once the words were spoken and the Asset recognized a handler and received a mission, they couldn't be over-ruled except by hitting the Asset very hard in the head.
Steve & Co. (or for extra trust issues, Tony & Co.) for some reason have to thaw Bucky out and take him on a mission or flee. The enemy has Bucky's code words and a bullhorn.
The only way to keep Bucky out of enemy hands is to say the code words and give him a mission before the enemy does.