No, architecturally there's no reason to do it on the client side. You're uploading a photo to iCloud, encrypted with a key that Apple controls. The only reason to use even a little bit of battery power to do the check on the client, and to do this elaborate song-and-dance around only notifying Apple if there are a certain number of positive matches, is that it creates the (false) impression that Apple couldn't just check your photos on the server side if they wanted to.

It's basically engineering with the goal of creating a perception of privacy rather than actual privacy. I don't really care that much about Apple policing what you upload to iCloud, but this disingenuous architecture does annoy me a bit, and there's also the added insult of having a device in your pocket that by design works against its owner (reminiscent of "treacherous computing"). These problems would go away if they just did the check on the server side.