A difficult part of writing for me is when a single sentence–especially dialogue–contains two tones. It sounds best as a single sentence, but ending with a period, or alternative punctuation, looks wrong. As well as this, using two sentences also looks wrong.
I can’t think of a great example right now, but I know I’ve wanted punctuation that doesn’t exist before. I’ve had moments where it would have been so useful to have a “;!” and a “;?” mark.
That’s when you underline.
And if you’re using software that doesn’t support formatting?
You just said you were handwriting.
Emphasis isn’t always possible with every utility, but a simple Unicode addition would work well for a variety of software, as well as be easy and readable on paper compared to underlines (especially if there’re words below). It’s also more accessible if you can’t draw straight lines to save your life. Like me.