My question specifically is: is there a specific reason why current web browsers don't offer an in-house Markdown parser, and what are the specific advantages/disadvantages that I may have overlooked in my consideration.
[1] Tested on a Linux system. I did not test Google and Brave due to privacy concerns. Safari also falls out and so does Microsoft Edge.
There's also several extensions to markdown, each with their own features and subtle edge cases.
You mentioned smaller files, but HTML is nearly as small after gzip/brotli, which your web server should be using for text-based resources anyway.