UPDATED 22.11.2022
It's been two years since the last update, so here's the updated working script as per the comments below.
Thanks to BryanHaley for this.
setInterval(function () {
video = document.getElementsByTagName('ytd-playlist-video-renderer')[0];
video.querySelector('#primary button[aria-label="Action menu"]').click();
var things = document.evaluate(
'//span[contains(text(),"Remove from")]',
document,
null,
XPathResult.ORDERED_NODE_SNAPSHOT_TYPE,
null
);
for (var i = 0; i < things.snapshotLength; i++)
{
things.snapshotItem(i).click();
}
}, 500);
Non-english users will need to change "Action menu" and "Remove from" to what YouTube uses for their localization.
YouTube appears to rate limit you after 200ish deletions in a short time - so while the deletions appear to work on the UI side, the videos aren't actually removed from the playlist. Absolutely infuriating.
Here's a modified version of the script that deletes 200 at a time, waiting 5 minutes between each batch to avoid doing any deletions that, uh, don't actually delete. With a 5000-video playlist, this should take 167ish minutes to run. Just put it on overnight or something.
The batch sizes and wait times are guesses, but they worked for me. You may need to run this more than once if any rate limiting happens - just reload the page and run the script again.