Matt Colville’s setting has a set of legendary swords called the Teeth of the Dragon. They promise cool abilities when the right character wields them, and even more abilities are unlocked as the character levels up.
I think this is a neat idea. It can make magic equipment as meaningful to players as it would be in-universe. Each sword is unique, and its story is told by game mechanics in a fun way. It also incentivizes the character to use this magic item for a long time. And each notable thing the player does with the sword adds to its mystique. This can be very cool.
I can think of a drawback though. When you bestow a Tooth of the Dragon upon a player, it’s a fantastic piece of loot. You’re basically rendering all other weapons moot in comparison. Why try to find a monster’s specific weakness to blunt fire weapons when your +4 Sword of Reckoning is specially crafted to destroy everything in its path?
If this legendary sword is the best weapon out there, why use anything else? It’s kind of like the DM telling you which feat to take. But what if I don’t like swords?