Treat it like you do customer support and automate it. Or is that not allowed?
Do you actually want automated take-downs? Isn't that what people already complain the most about on YouTube?
It’s a cache; it was going to expire after a TTL anyway.
No. But caching takedowns is not the same at all as YouTube takedowns. It’s very very clear who owns what data and after the takedown the site owner can modify the robots.txt and move on.