Introducing variant ARs against different types of attacks is for later.
However, the benefit of having alternative attack types is already there, based upon the situation. For example, your warrior may quite likely never stab with his sword, only making cutting attacks. But what if he is then in an area where he cannot properly swing his sword because there simply isn't enough room? Under the current listing, the broadsword may only be used for Slash/Cut attacks, not for Stab/Pierce attacks. With the new method, he can choose Cut or Stab, and if he has no room to swing the blade properly, he can still stab.....
Or perhaps he will feint a Cut, but make a stab instead (with the Feint perhaps giving a bonus to the base damage dealt if the foe falls for it...).
just because there is no obvious advantage from something, that doesn't mean that it cannot add flavor and/or be useful in unexpected ways...
For example, by giving a broadsword Stabbing damage, we can allow a character with a Rapier skill to use it as a stabbing weapon at a -2 to his AB in a pinch...