Totally agree. Whatever you think of Kahneman etc (Personally I think the original "Farmers vs Librarians" thought experiment in Bayesian reasoning was amazing for example) it's weird that to talk about a model you need to know about Thinking, Fast and Slow and what it said about system one/system two. Yes every name for a model is essentially jargon, but some jargon is better than others in terms of at least being somewhat understandable. When someone calls Jev a "decision model" it makes complete sense to me. That evokes to me the idea of a zero-shot classifier (ie the purpose of this type of model).

Not only does "system one" fail to do that (because it is an arbitrary classification as you have said) but it also ascribes to the model a type of thinking that humans do when we really have no reason to believe that is how the classification process works with this type of model. So if you'd read Thinking, Fast and Slow you might reasonably attach attributes of human system-one type thinking to this model that are not justified. So it's simultaneously opaque (if you don't know the reference) and misleading (if you do).

The numbering isn't arbitrary though. Theoretically it's the order in which those cognitive systems evolved. As for "System," well, I suppose you could call them Cognitive System One and Two. But it's usually pretty obvious from the context.