The problem isn't maneuvers, the problem is that maneuvers are pet abilities. There shouldn't be an animation attached to the Puppetmaster. The Automaton, when activating a maneuver, should get that little steam animation from the PUP special emote (as a kind of "kicking into gear" indication) so that it doesn't distract from the PUP's attack cycles.
I agree its a Pet Ability, But so is Restoring Breath, Bloodpacts, Avatars Favor, Assault, Snarl, ready, etc. If they update pup this way they'd need to update all pet jobs this way, which would take some work and im sure its probably nigh impossible :|

The Auto deals most of the damage, but the PUP's ability to maintain decent DPS is pretty important too. In situations where the automaton is just nuking, losing DPS because you have to freshen up your maneuvers hurts the PUP overall. Maneuvers don't need to be fixed, the annoying animation just needs to change.
I don't think my automaton has ever once Outdamaged me in combat on normal enemies or NMs :X

Unless we're talking about Ranged fights where I only use BLM automaton. ( i can think of Voidwatch as a possible example, bad AoEs, etc), then yah its possible.