No, you're getting that backwards in very important ways.
There IS a Department of War. The thing is, it doesn't have any budget or authority, and anybody working in such a department immediately gives up budget and authority.
It's not that the department doesn't exist. It's that it doesn't have legal authority to do anything, so if the president really wants to give up his ability to do anything that the Department of Defense can do, well, have at it.
He cripples himself.
This is absolutely one of those cases where we need to be calling out #Trump for, through incompetence, giving up the authority to do the things that his supporters want him to do. He needs to be called out as undermining his own political goals, as that is the way to start showing his base that they are backing the wrong horse.