Nice writeup! 
Can you describe the filtering you are talking about in a little more detail that people are relying on in their email? I’ve been around for a while too and have run mailman lists myself and participated (and still do) in many mailing lists, but have never encountered automatic filtering using headers. It seems to me that if someone subscribes to a list and they want to filter it into a folder in their email, they’d set that up for themselves on a list-by-list basis. You can do that with discourse too, right?
I think categories work quite well as a replacement for mailing lists, with mailing list mode enabled by the user or the user watching certain categories so they get emailed for every post. Maybe we need to learn some more as well about why you think organizing discussions into tags is better and worth the effort to get parity with how it works with categories already.
Edit: I am reminded of my old post about this, from back in 2014! 