This site, playbackloop.com, does that. Currently it's the only thing this site does! Watch your playlists in order!
Have you come across a Youtube playlist you want to watch, but the playlist is in reverse chronological order? You want to catch up on a youtube series but watching them from newest to oldest doesn't play well.
Well I work on my computer, a lot... I like to have Youtube playing in the background, usually picture in picture (with Safari on Mac) and I will catch up on my subscriptions and watch new playlists. I came across this Late Show with Steven Colbert Intro Monologues and it's over 500 videos long. I love it! This will keep me entertained for days! Anyway, as I was watching, it annoyed me that it was going back in time! I rather start from the beginning and binge watch in order, the obvious way.
So to help with my productivity in my work, I decided to take a tangent and built a tool to help me watch playlists in order from oldest to newest. Maybe I shouldn't be watching videos when am working. Will this make me more productive or less productive? Well anyway I can finally want these damn monologues in order.