I wouldn't even necessarily call Te a messy way of systematizing. In fact, due to Ti largely being a subjective way of thinking and thinking for the sake of thinking. It would make a lot of sense for Ti to often be considered to be "messy" by extroverted thinkers. Due to the fact that it's not really orientated toward anything outside of the Ti user's definition of knowledge and what is the truth to them.
Messy may have been the wrong word. But my point is that Te has to bump up against objective reality, as I understand it, while Ti does not necessarily need to do so. This isn't saying that it's incapable of aligning, but just that it's possible for it not to align.
Both orientations of thinking are systematizing, but towards different ends.
Yeah... T is a systematizing function, so I may have mistakenly implied that Te is not systematizing.
Wacky and nonsensical use of systems are the product of inferior thinking. While conspiracy theories are generally something that is attributed towards inferior intuition BTW. I would imagine that an Ti/Te type's weakinesses to generally be more alongside of using systems that are used to justify a generally misanthropic prejudice or something along those lines, but I have no way of clarifying if that is the case though.
A decent amount of the people who subscribe to nonsensical systems type themselves as NT's, especially introverted NT's. I have to either conclude that they are not "true NT's", which sounds like self-congratulatory bullshit on my part, or that it has something to do with being an NT. I think conspiracy theories and "alpha males" are attempts to use T to make sense of things that exist outside of the domain of T while having inadequate information and experience, and being unwilling to seek that information and experience out.
I suppose the attempt to use only Ti, and not use Ne to generate alternative possibilities, can explain the usage of idiotic systems.
I also think exclusive use of Ni might play a part in this, as well. I don't understand this function very well, but it seems to me that it could also be capable of generating craziness without needing to see if it reflects the way things actually are.