The script is well supported, it was introduced in 1999 with Unicode 3. Vertical writing is a concern of text rendering, so this has nothing to do with Unicode. https://caniuse.com/#search=writing-mode

This is still a bit lacking outside of Web pages, but generally work-arounds are in place which come with their own problems.

HN test: Монгол бичиг ᠮᠣᠩᠭᠣᠯ ᠪᠢᠴᠢᠭ᠌