CSS gives you multiple tools to solve this problem, if you don't use any of them then it's not really CSS's fault.
> Styling code near your semantic HTML tags doesn't get in the way
It does. When I'm working on functionality I don't want to see styles and vice versa. It adds a layer of noise that is not relevant.
If I'm making e.g. a search dropdown, I don't need to see any information about its cosmetic appearance. I do want to see information about how it functions.
Especially the other way around: if I'm styling the search dropdown I don't want to have to track down every JSX element in every sub-component. That's super tedious. All I need to know when I'm styling is the overall structure of the final element tree not of the vdom tree which could be considerably more complex.
> I've never seen a complex website redesign that didn't involve almost gutting the HTML either
Perhaps for a landing page. For a content-based website or web app you often want to adjust the design without touching your components.