I think it worth noting that in the days before desktop publishing (say, prior to 1980) underlining in book and trade publishing was really difficult. Sufficiently difficult that it just wasn’t done. Thus, proofreaders (the people) could easily use this difficult-to-do in print notation to represent something that was easy-to-do in print, italics.
For those old enough to remember, like me, try to imagine how a Linotype or Intertype operator would underline something. Yowza! And their employer would discourage the practice as well. Waaaay too much time spent for a marginal, and little understood, practice. Nope, italics it was.
BTW: I dislike underlined type. For you authors and graphic designers out there, italics provide the emphasis needed without disrupting the page color. Remember, books are not the internet and there are no links in books.