Now out here in Virginia, we only refer to these referenced structures as outhouses. The expletive part I've never heard in polite, country conversation. (Or impolite, come to think of it.)
To this ear, the former ("outhouse") is a polite and somewhat effete euphemism, the latter being the basic form.

Possibly WW and I differ on this because men are more given to euphemistic speech-forms when ladies, like WW, are present. ("When nature is calling, plain speaking is out / If ladies, lord love 'em, are milling about.") Perhaps this is a simple case of the familiar maxim, "Circumstances alter cusses."

"brick" __-house, implying: She's also got her feet firmly planted, if not on, in the ground. She's unshakable. ... Mae West comes to mind.

Here the analogy breaks down a bit. Mae's persona was unshakable but, unlike a brick structure, was emphatically not untippable.
In short, the name "Mae" was descriptive.