Premises:
1. YouTube's primary function is entertainment. Many people also derive educational and informational value from it, but that's incidental. Wikipedia and Google News probably serve that purpose better.
2. The most straightforward way to measure how well YouTube serves as an entertainment channel is viewer minutes. There are drawbacks to measuring per-session or per-view minutes (short term outrage spikes can backfire later), so it's better to maximize life-time viewer minutes. These can't be measured directly, but need to be modeled/predicted. But it's a refinement of viewer-minutes, not a fundamentally different metric.
Contention:
Maximizing viewer lifetime minutes is the best practical way for YouTube to serve it's primary function.
But what if I told you that 30% of users who stop watching YouTube go on to use a different media service, even though they could have watched exactly the same content on YouTube. Would you feel comfortable informing these people that they could watch on your site?
It could be that most people's goal in life is not to watch the maximum amount of YouTube.
One thing I've wanted since I saw a prototype Joe Edelman made for Chrome, is after a video is played, prompt the user for a rating, and a reason for the rating. Joe had a taxonomy of human values for this, but it could also be a freeform tag based system.
Then when you go to YouTube next time, you say that the reason you're at YouTube is to "increase my knowledge of machine learning." Or maybe it's Friday evening and you just want to "make me laugh."
Most people probably won't pick "make me outraged or scared.", but that does give good engagement metrics...