Yeah, sending a .md for client-side rendering would allow the client to reformat it more easily based on user preferences. Then again, Safari/Firefox reader mode already do an ok job with HTML for this.
But we could go so much further than reader mode. Users should have way more control over how content is rendered. But I'm something of an extremist. I don't really consider CSS/JS part of the web.
I don't really agree about CSS/JS, but either way, I've been in plenty of situations operating informational sites that just want to serve mixed text/image without worrying too much about how it's formatted. Unfortunately there isn't such an option. Regular HTML tags are supposed to do this, but most browsers won't format those in a modern-looking way. It'd save a lot of collective time if they could.
When those "informational" sites were normal 15 years ago, browser like Opera had user-CSS that you could just override, and had a number of presets. You could format the site to look like C64 BASIC.
The stuff you're talking about isn't about browsers its about the websites.
If you had a website that uses javascript to parse MD or any other markup, spit it out as trivial HTML with light DOM, client-side formatting can do everything you want.
The problem is that modern websites use patterns that workaround users' capability to customize the presentation of the website. They do not want you to look at their site the way you want.
Browsers can reformat clean HTML easily in theory, but I mean the defaults aren't nice, and most users aren't changing them. You have to use CSS to make a site look good by default.
I guess the best solution to that isn't browser-side .md rendering, though.
If browsers were easier to make, someone could experiment with content negotiating for markdown and rendering it client side.