I don't think so. I think it would be sufficient to document the exact markdown it supports and let the chips fall where they may. Yes, it would push markdown in a certain direction, but that's OK as long as it stays faithful to some variant most people already know. For instance whatever variant Github or some other major, main stream tool uses. And then just ignore the critics.

It'll certainly make some people angry, but if we try to please everyone we can't get anything done. And I suspect that it is the fear of not being able to please everyone that is the reason browsers do not have markdown support. It takes a bit of courage to say "this is the variant we'll implement".

HTML was originally said to be an application of SGML. It wasn't. It was vaguely inspired by its syntax and that is the only reason HTML saw wide adoption. Had they tried to actually implement anything close to ISO 8879:1986 we would NOT have adopted HTML for the web. Mostly because it would have been too costly to implement. (Anyone doubting that: have a look at the ISO standard. You can get it in what is essentially annotated form in Charles Goldfarb's "The HTML Handbook").

Of course, Markdown is nowhere near as complex. So this is where perfect is the enemy of good and we end up getting nothing.