It's mostly the links and images I have an issue with TBH, and I don't see much need for headings. Lists still just look like lists in plain text so they don't bother me at all. Same with blockquotes (which I think is just a > ?)
Part of my issue with links and images is that they're not easy to strip from the text. I could parse the markdown and then strip the html, or write some regex that would strip it, but don't think it's right that clients that don't want to support it should need to do that.