Meridia could've easily give you something other than a sword, it wouldn't contradict her character.
Clavicus Vile too.
And the f-ing GOD OF HUNTING doesn't give you a bow?
What do hunters use, HIDES. Do Hunters make bows, no in this game BLACKSMITHS make bows.
Its established lore. These are these Daedric Lords items of power, they have been around since Morrowind.