But the Markdown document doesn't actually need a parser to still be usable. Markdown as a whole imitates the conventions of typed text. The table formats would even be usable on an old typewriter.
extensions to markdown aren't markdown; that's why commonmark is called commonmark
not being able to tell which variant of a language is in use is one of the biggest problems for archival, and in particular various extensions to the microsoft word format (all made by the same company!) were what made jgc's archival work so difficult in this case
language extensions are an especially bad problem when there's no extension mechanism—because sometimes a pipe is just a pipe. but unfortunately markdown's only extension mechanism is html
It's called CommonMark because Gruber insisted. Not because extensions to markdown aren't Markdown®, which no one cares about, and not because it isn't markdown in the ways that matter.
Ironically, his objection was to the idea of a single and rigorous standard, you'll note that Git-flavored markdown never drew his wrath. And yet you're treating him and Swartz's implementation as if it was such a standard. Which it is not.