To be fair to us all talking about this, I am under the impression that the problem of “standardising” Markdown rendering is a big issue, and I recall it being worse in the past when Markdown was first spreading into different web applications. I’m a relatively new stakeholder, so I won’t pretend to have a full knowledge of the history here.
I’d advocate strongly for using markdown-it for both JupyterLab and nbconvert. As you say, it’s quite easy to create plugins, and it would make it a lot easier to write Python packages that deliver both nbconvert and JupyterLab extensions.
I’m sure that we’re on the same page at this point, but I would not want to enshrine markdown-it into the Notebook specification — just establish a semantic interpretation of what the extensions mean, and let the frontends Do the Right Thing™ 