For speakers of the USSR’s Turkic languages (Kazakh, Tatar, Crimean Tatar, etc.), latinization was therefore seen as harmful, because these languages are often fairly mutually intelligible with Turkish of Turkey, and a common-ish Latin alphabet would mean these peoples would be susceptible to anti-Soviet ideas coming from Turkey. Therefore, the Stalin-era language authorities not only gave them a new Cyrillic orthography, they gave each language a different Cyrillic orthography than the rest to fragment them even further.
In the case of Mongolian, Cyrillic helped better separate Mongolian of Mongolia from the mutually intelligible dialect of Mongolian spoken across the border in China.
That doesn't seem correct to me. Different languages require different orthographies because they have different phonetics. Compare the Latin script when used for English to German to Vietnamese to Turkish. Same thing with the Arabic script with Persian and Urdu. When tailored orthographies aren't used, the written representation becomes a poor representation of speech. Though even then it might not have been a perfect fit in the first place, requiring digraphs or diacritics. Or the spoken language can diverge.
And no, they won't ever get rid of categories. It's just that the phone variants of the site are very heavily geared towards a specific type of reader, at the expense of editors or other types of users. They have been trying to address this over incremental updates though, such as now showing talk pages.