The technical answer is because that functionality is explicitly disabled, as you can see from this HTML extract:
<div style="tab-size: 4" spellcheck="true" autocorrect="off" autocapitalize="off" contenteditable="plaintext-only" class="cm-content cm-lineWrapping" role="textbox" aria-multiline="true">
For the reasoning behind it, only @manton can tell us. Maybe he hates these features. 
Or, more likely, there’s a compatibility problem or something similar that’s the reason behind these choices. See, for example, this thread about an old issue between Markdown highlighting and the spellchecker.