A fourth case: Often, the lack of response to an older message is what prompts me to send another PM to remind someone I’m still waiting for them. I get a lot of notifications, so often I have to dig through my PM list to find a week-old message.
That said, I’ve installed a userscript that pulls out my PMs to a separate glyph anyway. I’d be happy to get rid of it if there was an easier way in core, hence why I’m posting at all, but if not, I’ve got a solution that works(-ish) for me.