The Tai Chi Classics say the sword and other weapons forms train the ligament and bones.
Training with weapons is an important part of a Tai Chi Chuan curriculum; because of their nature Weapons forms retain the faster flow and "fajin"or energy release that is an inherent part of the martial part of Tai Chi Chuan.
From a western perspective weapons forms act as a form of weight training and develop remote proprioception skills. The focus in weapons forms brings the player's awareness to the striking surface of the weapon and away from the hand.
The effect on the brain is an increase in the motor skills "map" which manifests physically in an increase of connections and brain size.
In connection with self-defense skills, it is highly unlikely that you will in a real life and death situation be facing an opponent who is empty handed or want to fight empty handed yourself. While it is just as likely that you will be using an improvised weapon and not a classical one familiarity with several types of weapons and their forms allows a Tai Chi player to match technique to what is in hand.