That's when ContentID and the non-DMCA takedowns started happening.
You hit on this in your first sentence. And this whole arrangement with Google is specifically to side-step those penalties. Your 'easiest solution' is for Google to return to DMCA takedown requests. I agree. I want that. I think most consumers and content creators would.
But Big Media doesn't.
I mean, how fast would Google move if a non-responsive take down resulted in the youtube.com domain being seized?
Instead, Google would rather have made their own job easier by standardizing 'requests.' There's nothing in the DMCA specifying that some standard, machine-readable format be used. To get the media companies on board with keeping the takedown request process as automated as possible, they compromised.
The easiest solution would be to create penalties for false takedowns of legal content, but this would likely just result in Google being sued for trillions of dollars by the media cartels to remove such restrictions under the argument that Google is aiding in piracy.