Yes, this has been proposed many times. It would be a fantastic way to address accessibility. There are some major caveats to be worked out:

1. Identifiers - You would need the ability to add things like id and class values to any potential DOM element node.

2. form controls - You would need to allow for interactive fields, like textarea, select, and input element types.

3. audio/video elements

4. non-functional elements, like span and div, would need to be allowed as necessary to provide opportunities for CSS layouts. These things should be painful to use in any code instance though otherwise markdown just becomes HTML.

5. Accessibility page structure elements, such as nav and main and footer, would need to be added as well. The role attribute would also be needed.

There would be no way to controls around semantic code structure beyond relation of headings.

Gemini (the internet protocol, not Google's stochastic parrot) is basically this.