Good points, Paul. While Scots today is still used for some imaginative literature, it isn't used routinely for law, medicine, or scholarly or scientific research. Unlike Standard English.

It's hard for me to imagine a form of speech as a true national language without that kind of cultural distribution.

Not that Scots wouldn't be perfectly adequate. But even with that sort of wide use, its written form would still look mostly like English - unless some government policy demanded the use of Scots synonyms and spellings for vast numbers of English words that the Scots already use.