From a practical standpoint, though, Arabic doesn't make sense - it's more complicated to learn, vastly more different from the alphabets of all neighboring languages (starting with the whole right-to-left thing), and most other Turkic languages use Latin-based alphabets these days.
But if the choice of Latin is dictated by pragmatic considerations, then it's reasonable to compare it to Cyrillic on the same grounds.
The original attempts to latinize (replacing Arabic) writing systems in those republics were, in fact, carried out by USSR, and it was very much a top-down thing, not some local initiative. USSR had a massive country-wide latinization campaign in 1920s for basically all languages spoken anywhere in the country that didn't already use Cyrillic. Long-term plans were to latinize everything, including Russian itself (this one went as far as a final proposal by a committee in 1930).
https://en.wikipedia.org/wiki/Latinisation_in_the_Soviet_Uni...
For Turkic languages specifically:
https://en.wikipedia.org/wiki/Ya%C3%B1alif
And part of a broader ideological push:
https://en.wikipedia.org/wiki/Korenizatsiya
It makes perfect sense when you realize that Soviet government, at that point, viewed itself as a first comer in a blaze of worldwide communist revolutions, that would ultimately produce a single worldwide federated communist state. Per Marxist dogma about industrial workers being the vanguard of the revolution, the expectation was that the center of gravity would shift to Western Europe once revolutions happened there. Communist utopias of that time period generally assumed that such unification would result in adoption of some common language, and that Latin script would be used for that language. So adopting Latin for Soviet languages made sense in preparation.
When Stalin abandoned the concept of "world revolution", and switched instead to "socialism in one country", with a heavy dose of Russian nationalism underpinning the new ideology, all this was scrapped, and (then already established) Latin writing systems were replaced with Cyrillic ones, from roughly mid 1930s onward. Those Cyrillic writing systems are the ones inherited by the Asian republics at the dissolution of the USSR.
Changing your official language to a new alphabet is pretty expensive thing (especially when your country's economy is collapsed and your country has extreme inflation). You have to change all official signs, texts and reteach whole population.
Another stupid thing Uzbekistan did is to publicly burn (literally) soviet school books while not having a good replacement. I remember looking at those burning soviet math books in my school's backyard.
And it's all done instead of what? Instead of:
1. Teach population of proper fluent English as a second/third language along with Russian;
2. Making competitive free-market economy without clan-type quasi-government monopolies which run by top government official's relatives;
3. Attracting and protecting western investors;