I think I have read this suggestion at Reddit: "Make people who wants to use API as clients pay. " The app doesn't have to have API key, user pays a very reasonable money to access Reddit with their favourite application. Obviously it would come with sane for human browsing limits and AI leechers should pay millions.
Just like a plain old radio station where you can access from web page for free but you need to subscribe for better AAC, high quality streams and standard VLC support.