So you're saying they're preserving organics merely in the sense that they built something out of organic construction materials? They're totally destroying their whole civilisations, killing their people etc. We are given no indication that they are being used as anything other than raw materials. I might at least at a stretch be willing to entertain the notion that this isn't totally illogical if they were uploading people's minds to some kind of computer database or something, but the Reapers and Collectors just babble on about genes and genetic compatability and stuff. If the writers intended for the Reapers to be actually preserving culture, intellect or anything other than the particular atoms that they were using at the time of their harvesting, they had plenty of opportunity to show and/or explain this, especially considering you have extended conversations with the architects of this plan.
If they intended to show this as an AI gone rampant or malevolent genie type situation, they really should have gone into more details. For example, the Leviathans could have tasked them with preserving organic species in some way, but the commands were written in such a way that the AI interpreted it in a strict sense, and considered it only important to preserve samples of their biological material, not their culture or anything about their civilization. This doesn't get around the flaw you point out yourself (and which I've lamented in the past as well) regarding the stupidity of essentially sending your biological preserves into open combat. It also doesn't get around the broader problem of why the Reapers could possibly want to use the biological materials as construction materials for new Reapers. It is implied that somehow this allows them to take on the characteristics of their hosts based on genetic traits and comparability. This isn't a logic problem, it's just abysmal science and writing. I can't believe they did something so incredibly stupid. The final irritation is how in ME1 it's all "we are beyond your comprehension" when actually they can summarise their entire existence and goals in a twitter post without losing any meaningful information.