They should, but they should also clearly communicate what content they consider acceptable and I think they should also notify the user and give them time to move their things out if G decides the content is deemed unacceptable. Especially if the content is not obviously and egregiously violating the terms of service and hasn't been considered a problem for the past seven years. Pulling the rug like that all of a sudden isn't cool.
If I offer to hold your grocery bag while you go to the restroom, do you think it's OK for me to throw it all away because after digging aronud a bit, I notice you have bought apples I don't like? What if I've been repeatedly extending the same courtesy for the past ten years and never had a problem with these apples until today? What if I advertise myself as a free bag holding service by the entrance to the restroom?
I think people should have the expectation that if a company (or individual) offers a service and holds on to your property (be it digital or physical), they should treat it responsibly and not just trash it all out of the blue.
> Clearly it wasn't following intent of the site.
That does not seem clear at all based on a reading of youtube's policies.
> And the user didn't really lose anything, as they still have the originals.
That's not something Google can decide or verify. Instead, they could help the user move their stuff out and that would ensure they still have everything.
But I like this line of arguing; I think copyright infringement is ok because the copyright holder still has their original copy which has in no way been affected.