Well, I guess one reason for keeping it public is literally to demonstrate to other nations that the US is prepared for this kind of thing - but I suspect everyone who needed to know that already knew...
"Of course, the whole point of a Doomsday Machine is lost, if you keep* it a secret! Why didn't you tell the world, EH?"
Given that JCS seems to have leveller heads than POTUS (witness their responses to his suggestions of persian gulf aggression or of domestic deployment), I find it reassuring.
"Gentlemen, you can't fight in here! This is the War room!"
Gutmang na kang du kombat xiya, fo xidawang da imbobo da kombat!
"Of course, the whole point of a Doomsday Machine is lost, if you keep* it a secret! Why didn't you tell the world, EH?"