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.
So, for the record, these things come into existence in the first place simply because someone, somewhere, starts using them. Language is something that drifts over time, and punctuation is no exception.
It’s a bit harder to do this digitally though since the glyphs aren’t just marks on paper.