When enchanting an axe, 99% of enchants listed are for a weapon. An axe is primarily a tool and secondarily a weapon and I feel the enchants it will list should reflect that. In Java Minecraft, this is the case and you can still add "Weapon" enchants to an axe with an anvil but you will never get a "weapon" enchant on your axe from the enchanting table. That feels like the right way to go about it...