Agreed with the assessment of the article, but I find Japanese to be significantly more logical than English/other languages I’ve learned. Just, the way it’s typically taught makes little sense usually. Recommend Cure Dolly on YouTube for some high quality explanation of the inner logic behind the Japanese language in a way accessible to western language speakers.
I think it's not significantly more logical than other languages. For example, there's no rational-designed reason to have different ways of describing the number of an object based on the object's qualities. "I have 4 books" and "I have 4 apples" shouldn't have different ways of describing the number 4. It's purely based off of organic growth and provenance of the language itself.
Blame it on the Chinese - Japanese didn't have that many "counter words" until Chinese influence increased that by an order of magnitude or more.
As for why you need them, Wikipedia points out that because there's no concept of singular or plural (in general, excepting words like "私たち" for "we"), you may consider all Japanese nouns mass nouns. And with mass nouns in English you usually have to use something similar: ".. loaf of bread" ".. grain of salt". The "solution" is not the same in English as in Japanese (you still use "one, two, three.." in English), but still, you can't just remove it. For Japanese there are other ambiguities which are resolved by the counter system as well.
But yes, the counters.. that's one of the bigger stumbling blocks I ran into early on. Learned the numbers, yay! Then learned that I can't use the numbers when I want to say how many there are of something.. I limited myself to the few where I can, as in the counter for flat thin items like e.g. tickets. "にまいください"