Why does the MarkDown italics mark-up work even within words, anyway? I think the situations where someone would want to italicize only part of a word are far fewer than those where one would want to use a word with an underscore in the middle of it.

I would think a lot less of a language that introduced an arbitrary limitation on its syntax like that. Italics of parts of a word come up occasionally and bold letters of a word more frequently than that. The language arbitrarily deciding it doesn't want to execute the formatting commands unless you do whole words the same would be irritating, confusing and inelegant.