Depth is harmless at ankle height and hostile at shoulder height. A 300mm cabinet hung over a 700mm passage leaves 400mm of clear width exactly where shoulders and elbows are, and it will be walked into within a week. The first question about any bathroom cabinet is therefore not what it holds but what height it occupies and who has to move past it there. A tall unit standing on the floor takes its depth honestly for its whole height; a wall unit takes the same depth only where the body is widest.
The over-toilet cabinet is the one most often got wrong. It has two clearances to satisfy and they pull against each other. The cistern lid has to come out for a valve to be serviced, which means lifting it clear before it can be tilted, so the underside of the cabinet must be above that lift and not merely above the cistern. Meanwhile someone standing at the toilet leans back. A shallow unit of 150 to 200mm can therefore sit low enough to be reached; a 300mm one has to hang so high that its upper shelf is ornamental.
A tall linen unit is the most efficient cabinet in a bathroom, because it takes a small floor area and uses the whole wall height. Depth decides what it holds: around 400mm takes a folded bath sheet lying flat, while 300mm only takes one on edge, which means unloading the shelf to reach anything behind. Placed at the end of a vanity run it reads as part of the cabinetry.
Wall and medicine cabinets are best judged by projection rather than style. A surface-mounted mirror cabinet stands 100 to 130mm off the wall, which is unnoticeable over a vanity because you step in towards it, and genuinely dangerous over a walkway or inside the arc of a door. The wall above a doorway is one of the few surfaces in a bathroom nobody is using, and a shallow cupboard there is often the only new storage a tight room has left.