Where I live,the majority of exhaust vents are placed on exterior walls. I don’t see why it wouldn’t work for you. Just be sure to have some kind of weather guard on there to stop rain getting in (basically, the slats on the vent cover should point downwards).
Same here (northern Midwest US) for new construction. Although, to clarify, they’re still generally routed/ducted through the attic and exit through an exterior wall.
Weird. Must just be one of those regional things. All of the ones I’ve ever encountered that I know of went out the roof. Good to know going out the side is normal somewhere though.