From today:
“Russian State Cult of Cyrillic Alphabet a Relatively Recent Development, Bagdasarov Says”
http://windowoneurasia2.blogspot.com/2018/02/russian-state-cult-of-cyrillic-alphabet.html?m=1
The question of alphabet is purely political in this context. Your link correctly points out at cultural aspect of script usage but it fails to explain how exactly Latin would help Turkic people to better exercise their identity. Latin is more alien for Central Asia that Cyrillic for sure and the idea of it is to inflict a cultural split between Russia and Central Asia realigning the latter to China and Muslim world.
Why not Arabic alphabet if so?
I also fail to see the benefits of all the above for the West pushing the agenda in the first place. It makes about as much sense as if Russia was campaigning in Southwest for switching to Spanish ‘for Hispanics to better exercise their identity’.