Its not going to break anything if you do it any more than the rest of mythic.
Mythic Rules somewhere wrote:
Legendary items are always non-consumable magic items, and are typically magic weapons, magic armor, or magic items that take up an item slot (though there are a few legendary items that don’t take up slots). Even vehicles and siege weapons can become legendary items.
If that's the only place that says what can become a legendary item, then it seems the door is wide open.
On the other hand, You need to pick legendary item twice to turn a mundane item into a minor artifact.
You could rule that you need two picks to claim Dawnflower's Kiss as your legendary item, but...that's giving up a lot of power for little reward and will likely just make the player pick some other sword.
So its probably worth just to let it happen.
