Kiwi6 is a little broken, but it's currently the best option because it doesn't rely on YouTube. YouTube-based players still load the video itself, not just the audio, which kills internet speeds and takes up way more data than necessary.
So here's how to make a playlist work:
1. Pick a playlist and scroll down to the bottom of it
2. Scroll back up
3. Click a track, NOT the play button
4. Congrats! It should be playing now.
Note: the shuffle feature does not work. It just...doesn't do anything. I can't fix any of these bugs because I don't own the iframe.