So, if I had your layout with a water heater in my basement, every time I went into the master closet, the motion detector would turn on the circulating pump. See my point now?
Our master bath has an open concept. It shares a 22' wall with the master bedroom and is about 14' wide. The entry door is on the end of the 22' wall, with the shower on the left 14' wall followed by a freestanding whirlpool tub on a 18" elevated pad. This engineer didn't like that as it's pretty impractical, but the home decorator (aka wife) loved the look. The double vanity is along the 22' shared wall and the toilet and bidet is kinda in the corner past the vanity. The towel closet takes up 6' of the 14' wall and is only 18" deep. My wife's fold down drying racks for her sweaters and delicates is opposite the double vanities. We rarely close the bathroom door being retired and it's only us in the house. And when the kids and grandkids come over, we usually only close the bedroom door. With a bathroom that large, hardly ever closing the door, and keeping our medications in their bottles, we don't really have a problem with humidity.