The real question that should be asked is: what would the inclusion of the hypothetical weapon known as the broadsword add to the game? Right now, D&D categorizes "swords" into some fairly broad categories, and has applied labels to those categories for ease of reference. To break them down:
a one-handed, light, straight bladed piercing sword - shortsword
a one-handed, straight-bladed slashing sword - longsword
a one-handed, curved slashing sword - scimitar
a one-handed, straight-bladed piercing sword - rapier
a two-handed, straight-bladed slashing sword - greatsword
a two-handed, curved slashing sword - falchion
And so on. But these are just terms used to describe weapons with certain characteristics in common, and subsume a broad category of items that had different names, but generally similar characteristics. What is being described as a "broadsword", to my mind, should fit in the "one-handed, straight-bladed slashing sword" category, and hence, I wouldn't see a real need to include a new weapon designated as the "broadsword", just call your weapon a broadsword and use the "longsword" stats.