The problem with client side verification is it dosent take much have the system look at all local files for verification, not just the files being uploaded to iCloud.

Now that Apple has some form of client side verification, an authoritarian government with enough economical clout can preassure apple into extending the system to look for things beyond child pornography. The govt could even just provide apple with their own hashes which may or may not be CP and mandate that Apple verify these hashes too. So in the end it all depends on how well apple is ready to push back against such government and if they are willing to take a hit to their profit margins by being effectively banned from a country