Imagine if something from the government regime in those countries sponsored such a site. Would the US be willing to get in a massive geopolitical argument with Russia or China over some copyright disputes?
"We're the host here, we're subject to DMCA safe harbor, either file a proper claim (to be evaluated by our counsel to avoid bogus complaints from a Mr. Russel, first name Jimmy) or get lost."
Even with the 10 days wait and counter-notice, this is strictly better than the nonsense system Youtube uses where people can have their content pulled down by trolls with no consequences.
Google, on the other hand, can't deny the takedown as long as all the requirements are met (AFAIK, IANAL), and besides, good luck paying for enough lawyer time when you're getting hundreds or thousands of requests per day.