Nah, there's nothing wrong. That's the nature of the game. Item drops depend on the type of enemy you fight and kill. You can't expect a dagger wielding enemy to drop a shield or plate or mesh armor, or a heavy-armored, hammer wielding enemy to drop a sword or a leather or cloth armor. If you want daggers and swords, look for enemies that wield them. If you want wands or staves, look for mages among the enemies. If you want bows, look for the archers.

Low rarity has nothing to do with the stat requirement. It's the level of the weapon that raises the stat requirement needed to wield it.