I agree, your solution here would be good, but I don't know if the Devs are capable of such changes in the logic underpinning the way the game's logic works with regards to pets and all mobs in the game.
My recharge time solution does work. I made a similar suggestion on another Ourodev server and they implemented the change and it worked out very well. The Umbra Beast ran into melee more frequently (which is its preferred combat posture) and it used its other powers much more effectively. Most other control pets have fewer powers to draw upon, so a change to the logic may not be needed to fix this one issue for this one pet.