xkcd

48" / 5 = 9 3/5" = 9 9/15" ~= 9 9/16" or 9 5/8". Dividing by five gets a little messy, but I divide by 2, 3 and 4 a lot more often than I divide by five. Thing is, that works out to be some pretty narrow doors, like, middle school locker narrow. You can indeed contrive scenarios where the math is ugly, but inevitably the cabinet you'd make would also be ugly. In actual scenarios you face in the real world it has a way of working out.

I'll give you a real world example. I recently built this dining room cupboard and hutch. The absolute overall width of the cabinet is 4 feet at the tabletops. The tabletops overhang the edges of the carcass 7/8", and the legs are 1 3/4" thick. So the area between the legs that the doors fill is 3' 6 3/4" (4' minus a total of 5 1/4"). The upper doors are 1' 2 1/4" and the lower doors are 1' 9 3/8". In reality each is 1/16" narrower than that to allow for some space for the doors to swing open and closed. The drawers have a 3/4" thick bulkhead between them, so each opening is 1' 9", and the drawers are 1/8" narrower than that to allow a 1/16" gap on either side so each drawer is 1' 8 7/8".

The leg dimension was chosen so I could have two layers of 3/4" boards, one for internal structure one for the outer rails, doors etc. and still have the legs stand 1/4" proud to make the legs look like legs (which they are; they're genuine posts) and to hide any impreciseness in fitment or milling of the rails, doors, drawers etc. The top overhang on each side is half of the leg's thickness, and then every dimension after that comes from the plan of the cabinet.

Tell me that wouldn't have been a pain in the ass to do in metric.