e.g. if they made it so their software simply refused to upload a photo and inform the user why it refused to upload it, then there's no privacy issue (at least not until they do add a backdoor later on).
The main problem is the precedent this sets: on device scanning is now possible.
Before this, if a government asked Apple to scan all the phones for something, Apple could say "we're sorry but we don't have the capability " and they could not be compelled by legal means.
Now, a large part of that argument has been eroded. Apple may have added in a few hurdles, but the first crucial step of on-device surveillance capability has been installed and is on path to being normalized.
It doesn't matter that they don't do this yet. We are undeniably closer to direct phone surveillance than we have been before.
That proposal probably wouldn't work for a lot of reasons though. The largest blocker being that (IIUC) the NCMEC won't share a DB of offending signatures without NDA, so Apple probably can't load it onto consumer devices.
i.e. my iphone told me this photo was in the database, so I'll start adjusting it until it 'passes', and them I'm free to share it without detection.
Similarly, governments could take a known image they want banned (say of a national embarrassment), grab some CSAM, tweak the signature on the CSAM to match the photo they want banned, and add the tweaked photo to the CSAM DB.