My Kindle Paperwhite 5th gen is rooted and runs KOReader.
It's not a great solution - you still have very little freedom, Amazon frequently patches root methods - and you might be waiting months for someone to find a working root method, and if you accidentally update - bye bye, root/KOReader.
Yeah, I think KOReader started out for Kindle first, and then added Kobo (and then other things - works on Android for one, and KOReader is typically what I use if I'm reading on my phone too). I just went with Kobos from the start because it seemed like there were fewer problems with Kobos w.r.t. getting locked in/out of things than with Kindles, though Kobos are harder to get hold of (outside of Canada, I suppose) than Kindles.
It's not a great solution - you still have very little freedom, Amazon frequently patches root methods - and you might be waiting months for someone to find a working root method, and if you accidentally update - bye bye, root/KOReader.
But it is a solution.