Adding the ability to cast while moving would require rebalance of BLMs damage - spells would need to do less damage. Is this what you want? Perhaps a stance that allows mobile casting but that reduced damage by 20%. This could actually be a good trade off in some instances.

BLMs already have one of the highest DPS outputs. Contrast that with BRD who is the only real mobile DPS in the game. BRD needs to constantly be attacking while moving to keep up with the turret DPS.