I very rarely see this style -- which comes from "Setext", IIRC, which might be patient zero of the "human readable plain text markup styles" -- in the wild anymore, and I suspect it's probably for the reasons you're describing here. I almost never use it myself, except in contexts where the "source file" is just as likely to be read as a rendered HTML version. README files are a good example.

> In some editors/IDE, the underline even gets highlighted / boldfaced, thereby exacerbating this effect.

I think a lot of editors just don't know about this style of heading, but they do know that a line of three or more dashes is used to create a horizontal rule, so they're trying to highlight that.