First off, I hope this question is not too offensive. Discussing technicalities of a genocide will certainly disgust some. I am in no way trying to condone nazi crimes. I am also not sure whether it makes sense to search for rational thought in genocide. Here goes anyway:
Nazi death camps used shower heads to introduce a gas into the gas chambers, thereby killing people. The gas used was Zyklon-B, an industrial product produced by a single supplier, and likely relatively expensive. It also meant that the gas chambers had to be aerated for a number of minutes before soldiers or forced laborers could enter the gas chambers to drag out the corpses.
Why didn't they simply use CO2? It's a byproduct of basically any fire. It's cheap and could have been produced on-site trivially. It's also part of normal air and only toxic in high concentrations, likely meaning less danger to soldiers.
I have to admit that I'm curious about something similar; the death camps and ots mechanism seemed highly inefficient, but the fact that I have to preface any questions on the topic with how much i detest the actual concept made me conclude that it's probably best not to ask. That's the annoying fact about being interested in finding efficient technical solutions while also hating nazis and everything they stood for.
Think of it as less of a pure killing machine and more of a system that is supposed to extract all valuable items and labour from humans with the end goal of them not surviving. The death camps were always embedded in a system of labour camps, and most of the time those who couldn’t work (anymore) were the ones getting killed. Towards the end of the war this started breaking down more and more, as well as never working perfectly to being with.