There were some gaping holes in this episode, some as wide as the maw of that DDM.
First, the DDM was designed as a planet destroyer, digesting the leftover planet rubble as its fuel. A starship is a significantly small item in comparison to a planet. For the device to navigate and "swallow" a starship would probably be more effort than it is worth.
We don't really know what the DDM was designed to do. All we have is Kirk's frankly rather far-fetched guesswork. If the machine really was a berserker designed to erase civilizations, then it would make eminent sense to attack starships in addition to planets...
Second, the DDM is designed to defend itself. If a starship attacks, it will attack back until it no longer measures any power levels posing a threat. As such, the best course of action would have been for Decker to power down the Constellation and wait for sufficient distance from the DDM to then power up and get out of there.
Many a submarine movie, a cloakship Trek episode, and recently also Matrix, reiterates this theme: going quiet is a good idea if you can do it fast enough, but it costs you your life if the enemy has already seen you and behaves against expectations. I doubt Decker would have been ready to disarm his ship when the enemy bore down on him: it would call not only for nerves of duranium, but also for extremely reliable intelligence on how the enemy behaves. Decker probably didn't have the latter...
Logically the only way to do anything to the DDM is by sending a bomb down its intake port, whether its a thermonuclear warhead or a matter-antimatter device.
Even when said intake port consumes incoming matter, including planets, with ease? The maw might have been the most impenetrable part of the beast for all Decker and Kirk knew, until further analysis. It sure was worth a try, but it was also one of the riskiest maneuvers Decker or Kirk could attempt - the enemy might have been vulnerable there, but it was also deadly there, and harmless from any other angle!
Remember when Kirk was the last member aboard the Enterprise in "This Side of Paradise"? He distinctly stated that one person can't run the ship.
Running the ship, and piloting the ship to a suicide dive, are completely different things. I'm convinced I could navigate CVN-65 to a catastrophic collision with a San Diego pier with zero training if I were handed that ship all powered up and pointed in the right direction. I sure as hell couldn't get the ship going if she were idled and moored on said pier.
There must be a continuum of things one can do with a starship, from a single-person kamikaze run, to a five-person interstellar hop, to a fifty-person refueling, to a hundred-person combat sortie, to a 300-person prolonged combat sortie that involves repairs, reloading and casualty replacement.
It is interesting that there was no mention of trying photon torpedoes. Weren't they already put to use in earlier episodes?
Yeah, torps were first season stuff, and this was from the early second.
Yet Washburn reported that "somehow the antimatter in the warp drive pods [of the
Constellation] has been deactivated". Supposedly, this would preclude torpedo use if it happened to the
Enterprise, too.
The DDM then proceeds to hit the
Enterprise while her shields are down. Warp drive becomes useless at that point. We might thus speculate that the hit involved this nasty antimatter-deactivation effect, rendering the torpedoes useless.
Timo Saloniemi