I used to use typora; it does have a really nice convert web->markdown. I think that it is done by some javascript or something because the other tools that have comparable quality I can think of off the top of my head are obsidian, joplin clipper and a couple of firefox extensions. I agree that in my experience pandoc and a couple other cli tools didn't produce such nice results.

I also think in all those cases the browser is doing some of the work because it renders the page, discards a lot of irrelevant stuff, then you copy/convert just a selection portion of what's visible. Whereas if you, for example, grab a raw html page through curl and send it to pandoc, none of that is done. You probably aren't using Select All when you copy a page to typora, but pandoc would be faced with the entire page. I don't know if there is a way to access the Reader View from the terminal but it would go a distance to cleaning up your pandoc conversion if you could start from there (for those sites on which it's available).

I tried and failed to do the same thing but it's not markdown's fault. No matter how many bells and whistles markdown would get, the issue is in the conversion from html part.