I don't think they have any qualms about shutting down YouTube but I think they're afraid of the backlash. It's such a unique treasure trove of cultural significance that is not out of the question for the US government to step in and tell them to put at least some of it in the Library of Congress or to work with other organizations to preserve it. And they'd rather let it run than be bothered.
I've heard a theory that says that Google isn't interested in any of their products for the product's sake. They're all data-gathering experiments. Once they're done mining that particular kind of data they shutter the project. If they ever need to revisit that category later, they make another similar product.
It would certainly explain why they shut down certain projects in the face of commercial success, or why they keep revisiting the messenger app over and over in different ways.
It would also explain their inept attempts at monetizing YouTube. Keeping an experiment alive past it's expiration date is unfamiliar to them so they have no idea what to do with it.