Categories are metadata. Why edit in the page when you can edit outside it? See how HotCat (or VE) has led the way. Put them on Wikidata? (how many things could be made into metadata?) Are a lot of them not just wikidata query results already?
Cats are old system.
Use tags instead? (Non-curated), and have categories as a way of editorially picking out the intersections of tags which make sense for humans?
Do this and the distinction becomes ambiguous. It's already very confusing in wordpress, which does this.
Previous discussion about page properties in general: https://phabricator.wikimedia.org/T55508
You can't (yet) kill them with fire though since they're still quite instrumental for /editors/, many of which base their entire workflow on them.
You could probably kill them more easily if watchlists were more flexible and allowed people to track groups of articles they're interested in in a way which makes more sense.
[Note: I copied and pasted this from an Etherpad during a Wikimedia hackathon in 2015 and these are not my words.]