Cyrillic alphabet corresponds to Mongolian phonetics sufficiently well, this is more a political decision dictated by shifting international landscape where Neosoviet Russia falls increasingly out of favor. Mongolia will not swap one writing system for another, they plan to use both Cyrillic and Mongolian script in official documents after 2025.
Old Mongolian script brings fundamental complication when viewing it from our era's high ground: it's vertical. And, unlike other historically vertical-only scripts, it simply cannot easily be adapted for horizontal use. Hence rendering difficulties and incomplete Unicode support galore. That alone, though, helps to distinguish it visually from scores of other writing systems.