If I worked at Apple I would do this: have developers create optimized apps that have a split-screen version so that multi-tasking is incredibly fine-tuned, and make the quality of this version part of the approval process if a developer chooses to make an app split-screen ready. Boom. (Feel free to contact me to work out a deal to purchase this idea, Tim.)
Genuinely curious, on what scenario would you want to watch a YouTube video playing while you doing something else on the screen? Sure someone could find it useful but personally I have tried on my galaxy S5 and I thought it was a bit of gimmick.