The issue is that, unlike slavic languages, those particular turkic languages lose as much or even more detail by being transcripted in cyrillic.
The biggest difference is that Latin scripts tend to create new sounds by adding diacritics or digraphs while Cyrillic scripts tend to create new letters — IMO the second way is better for non-Slavic languages.
Ц -> Z
Ш -> Sch
Ч -> Tsch
one could argue that german should also have one character for the "sch"-Sound instead of 3.
The postfix-h notation was a good idea, but the fact that e.g. "ch" is interpreted differently in English, German, and French derails it instantly :(
OTOH to type fast, you might want a more ergonomic input mechanism. (But I won't dive into the rabbit hole of really ergonomic keyboard layouts; if you're curious, search for KMonad, and think about e.g. the convenience of having modifier keys right in the home row.)
I happen to write in Spanish and German, for which the us-international layout is just perfect. But I did customize my xkb for some other keys, and I used to use kmonad before.
No need to strike for DOS compatibility anymore.
But it was invented too late, and lacked an expansionist empire, or a widespread religion, to bring it to enough neighboring peoples.