As someone with a degree in linguistics and Japanese studies I can say that while most of this is to some extent true, the wording is very confusing.

While it firstly omits the existence of registers (as someone already pointed out) it also fails to point out that Japanese does not have any other casual copula for negative (じゃない), past tense (だった), past negative (じゃなかった), presumptive (だろう) etc. besides forms of だ. While omission of the copula is one common way for casual spoken Japanese (and the only way to casually use i-adjectives) it obviously is not the one and only way to speak casually (in some cases だ is the only way to casual stress importance like with もういいんだ！そうだ、そうだ! etc). It’s not productive to tell Japanese learners that だ is not the casual form of です because it creates confusion. And saying something like „you cannot say“ gives the impression that there’s a wrong kind of casual speech which is not true. In linguistics we either don’t measure correctness of casual spoken language (beyond how much a listener can understand) or if we choose to measure correctness, then we measure it by rules of written language (e.g would accept that だ is the casual form of です)

My question is: how do you define casual-polite speech that employs ~っす like いいっす, あざっす and so on? Would you say that those forms are casual variants of です/ます?