Hmmm... I always thought the akumas only stayed powered up as long as Hawk Moth was transformed by his Miraculous, but maybe I'm wrong. He would still have to be Hawk Moth to charge up the akuma (infusing it with dark energy, turning the white butterfly black) and send it out. I guess maybe then he could transform back into Gabriel and wait for the akuma's power to infuse some object he carried with him. Normally, Hawk Moth isn't going to akumatize anyone unless he's there in his lair overseeing their actions, and goading them by making suggestions ("Grab their Miraculouses -- NOW!!"), but I guess if he akumatized HIMSELF (as Gabriel) then he gets the advantages of physical superpowers (which he doesn't seem to possess as Hawk Moth -- only telepathic influence). But if he HAS the ability to give himself physical superpowers by akumatizing himself, it makes you wonder why he didn't do that in the first place. I always presumed he *needed* those pawns to manipulate because as Hawk Moth, he himself has no PHYSICAL superpowers (and possibly isn't even ABLE to leave his lair while transformed).
The only other possibility that occurs to me is that Hawk Moth may actually NOT exist in any sort of physical state, but only be some kind of multiple-personality splinter persona existing within Gabriel's mind (but his mental powers and ability to manipulate dark energy is nevertheless very real). That raises the possibility that Gabriel may not even be aware that HE is Hawk Moth. What I'm imagining is this: when someone who was not Chosen as the user of a particular Miraculous (we KNOW that he was NOT Chosen, and Nooroo only grants him power unwillingly, although the rules of the Butterfly Miraculous compel Nooroo to obey its holder) attempts to use it, it instead fractures their mind, creating an evil doppelganger based on all the dark impulses that an ordinary person might never act on -- in other words, it frees those dark impulses from any governance by conscience, and creates a separate personality -- in this case, Hawk Moth.
What do you think?