Ah, you're right about music... I guess I've never tried videos.
For music, pause is it though... or reboot if it's that big of a deal. I do admit that it doesn't make sense to not have a "Clear Playlist" option, but it's never been that big of a deal.
I've grown on it... I have a large playlist that I put on random and use in the car, working, exercise, etc. I just start it up and let go for the week.
Download the free app "Stop the Music". This stops all music that will still stay loaded using some of the other methods. This is what I found works best. Keep it on your start screen and BOOM you're done.