I am thinking of painting the beadboard wainscoting in my 1/2 bath black.
The fixtures are white and the floor is b/w hex mosaic. Would you paint the rest of the trim in the bathroom white?
In a basic room I usually keep trim the same color; wainscot, door/window casing, cabinets and and crown.
In a small half-bath, especially with a dark color it's an "it depends" answer. Depends on sight lines, lighting, how much "trim color" versus "wall" or "non-trim" color.
So..."it depends" means I really can't give you a definitive answer on this and thus I'm tossing the paint swatches back into your corner, as it's really dependent on your space. It can be done. Nothing wrong with doing it. But it depends...
If you need to break things away and use other colors, often times the cabinets will be the first to be broken away, either through necessity or design. A different finish (stain for example) or a different paint color.
Next will be the crown.
Black can be difficult in a small room because it eats light. It can be used, often to dramatic effect. But it devours lumens.
I'm all for strong colors...or strong "non-colors" depending on how you view black. My office is painted black; black wainscot, black window/door trim, black crown, black floor-to-ceiling bookshelves on one wall, and black file cabinets and high wall cabinets on two other walls. The upper walls are beige or cream-ish cork with a bit of cranberry red in them. But it's larger than a half-bath.
But the beauty of paint? Things that don't quite work the way we envisioned can be repaired with a gallon of our next best guess at design happiness.