They actually started killing jews by shooting them in the head, exactly like you said. See those mass shootings: Babi Yar, Rumbula Forest and Ponary.

The problem was a direct killing like that was too heavy on German soldiers, so they needed another method where killing is less direct and more "dissensitived", that's why gas chambers were created.

Besides, whole holocaust didn't make any sense and analysing it from economic standpoint is pointless. Even when Germans had logistic problems and withdrawing from the frontline, because Soviets were approaching, they still continued to use rail and lots of resources to continue the holocaust, even though their army really needed those resources.

Hitler was not driven by rationality, but by his ideology and it was the most important.

Camps were differing from each other, some of them were death camps some of them were labour camps. In labour camps people lived longer but also died out of hunger or diseases.

I see you already know answers to all your questions though, so I doubt any of that will change your thinking