Now the underling is telling me they are going to run the pipes down the
corner of a closet below the new bathroom, and case it in with a fake
wall.

I consider this a lame shortcut. He kept telling me it's not a problem
to run pipes in the walls, now he doesn't want to do it? Well,
obviously it's not if you're just going to run the pipes down a closet!!

Am I being unreasonable to protest this move??

Is the *case* being constructed in "the closet" or is there an existing
closet that will then have a small corner "cased"? In any case running
pipes through a closet is not "abnormal". That is how my upstairs bathroom
is supplied in my (1970's) house. It is actually a convienance as I can get
at all my plumbing in my house because none of it was put "in wall" - yet
unless you go routing around the back of the one closet you'd never know the
difference. YMMV.

It's a cedar closet, my wife is worried it will add a 'moisture' factor
to the closet. Cast iron drop, copper supply. I don't know if my
wife's concern is valid or not.

He wants to put the case in the corner just inside the door of the
closet. It will take up from the inside of the door to the wall.

I think I will ask him to show me why they can't go down inside the
wall.

So - to answer your question. The downstairs cedar closet already
exists, and the case will be built around the new pipes.