The fact that it is special? All of this is arbitrary, that doesn't make it wrong.

Italics is the most important of those styling options for formal English writing (eg MLA style). Underlining was traditionally used a as substitute if italics were unavailable.

Subscripts and superscripts should probably work the same way as italics. They're just not as top of mind for me because I don't use them as often in my day-to-day life (and when I do, I often use the unicode characters).

I could see an argument for treating bold and underline this way as well, but I think the case is less clear-cut. Boldness is more likely than italics to be used for visual styling as opposed to semantic meaning.

Yup, bold is mostly used stylistically for headings, titles, stuff like that. (And sometimes as part of link styling, especially with a lighter link color.)

Virtually the only time it's used within text is in a textbook-type situation, where the first use of key terms is in bold, but subsequent usage isn't. Which isn't helpful/relevant if you're copying a passage from it -- just because it was the first usage in that book, doesn't mean it's the first usage in your own document.

And underlining doesn't really exist typographically except for links. It's always been the handwriting/typewriter substitute for italics. It has no established meaning whatsoever -- any non-link usage of it is idiosyncratic, which is usually not something you'd want to preserve.