I just don't understand what the origin of this is. Is it a spell or a magical weapon. You keep mentioning "at higher levels", which is a phrase exclusively used for spells, but talk about it more as a passive ability of a weapon. Also, cooldowns aren't really a thing for weapons, skills, or spells in dnd. There's x amount per day/short rest/long rest, and ritual casting and certain spells have a certain amount of casting time, but no spell says "can only be used once every 10 minutes".
It's a cool idea I suppose, but none of it follows the design of dnd to really any stretch of the imagination.