Do you actually want automated take-downs? Isn't that what people already complain the most about on YouTube?

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.

So yes, takedowns here are fine.

It’s a cache. Relatively speaking, who cares

It’s a cache; it was going to expire after a TTL anyway.