- GitHub-flavoured Markdown
- CommonMark
- etc...
On top of that, there isn't even some meta-standard which would allow hashbang-style preambles/doctype declarations to determine which version of Markdown is being served.
So, between the fact that there's no fixed de-facto standard and no de jure standard syntax or feature set recognized by any of the major standards bodies (IETF being one of these), it would be impractical for browser vendors to implement support for Markdown.
Finally, the standards that browsers implement take time both while being defined, as well as while being implemented; these are things that will be seen by billions of people worldwide, and there's extremely little room for error, so revisions are always necessary at every stage in development. For example, work on HTML5 can be traced back as far as 2004, meaning that from inception to release, development took about a decade.
For some more specific reference points:
Web Applications 1.0, as it was then, first defined the parser some time between February 2006. It first shipped in a browser (as the normal HTML parser) in Chrome 7 in October 2010. The parser was in the latest release of every major browser with IE10 shipping in September 2012. In a sense, therefore, when it came to parsing it took under seven years.
What? All of today's browsers can trace life back to before standards existed and they are constantly adding experimental, non-standard functionality.