The downvotes are trickling in, I'm assuming, because of a misunderstanding on my behalf. Is there anything I can do to improve this post?
I think it's a combination of two things:
You're advocating a particular prescriptive viewpoint. The community here tends to be prefer answers being as descriptive as possible.
More specifically, while you do mention 〜ないです is used, you claim 〜ません is the "proper" form. There are certainly people who believe that. But it's not a useful model for understanding the usage of the language. The descriptive model would look at when what form is used where, and try to identify a rule like "In speech, 〜ません makes for a hard negation, while 〜ないです focuses on making a soft statement. In writing, 〜ません is preferred due to being the more formal form.", or something to that effect. On top of that mentioning that some people consider 〜ないです to be incorrect is of course fine, but suggesting it to be incorrect yourself makes the answer non-descriptive.
The above point alone probably would not cause the downvotes. Compounded with it is your writing style. Let's look at some examples:
This is false. The polite form of both the negative and positive informal forms are the ます forms.
At first glance, it seems like you're claiming that 〜ないです is not a valid way to make polite negative verbs. Upon closer reading, it seems that's not the case, but it's certainly confusing.
While being close, and used frequently colloquially, they are not on the same level of politeness.
This seems a bit hand-wavey for what should be the core of the answer: the differences between the forms in detail, no?
They are, in the same way that "食べないです" and "食べなかったです" are allowed, however, as they do not share the similarities with い-adjectives, they have not garnered quite the same following (see: What does っす at the end of a sentence mean?. They sound like they would be less correct; less natural.
This is probably the most problematic passage in the whole answer. I think I understanding what you're trying to say: "〜ないです is a relatively new usage in grammar, using です in an unprecedented way; 〜るです would be just like that!"
Yet, the fact is that 〜るです is almost completely incorrect, while 〜ないです is extremely common, so your usage of wit here makes for an answer which buries the main point that no, 〜るです is not in common use.
And it's not just the fact that it buries the point. When a reader (especially one who knows Japanese well) thinks about why you worded it like this, it feels very much like "I know the history of this new-fangled 〜ないです contraption that the ignorant kids are using, and I will use this answer to show that off instead of directly answering the question."
I'm sure I made some claims about how your answer reads in ways you probably didn't intend. I certainly often write answers that read in ways that I don't intend (this one included, perhaps :-). But, this is the interpretation of it that stuck out to me as something that would annoy someone enough to downvote it.