Executes are less about skill than they are about flavor. Why does NIN's Mug ability give you additional items if you use it as a finishing blow?
What if your avatar form functioned like a mount outside of combat? It would have no impact on min-maxing, but it would be fun.
Multiple posters in this thread have pointed out what the stock formula for melee dps is. I would rather see them take a bunch of impractical ideas that we haven't seen in game yet and try to make them work, than to see them start with the template and then try to make the job feel different from dragoon.