Even if done locally, it's still creepy.
If any kind of metrics leave the phone's chassis as a result, then its quite creepy, but I was operating under the assumption that they are not.
Of course, there is also a real issue with the fact that, as closed source software on a locked down platform, we can't know what happens next. But that is just part of the deal with iPhones; there is already a lot of data like that (eg, I'd expect the US uses iPhone GPS data froom targets to hunt them down).
[0] Not sure what the feature actually does because nobody has posted details here, so there is some guesswork here.
If it detects cat pictures, what evil thing is it going to do? Label it as a photo of a pet (I don't even know, I don't use a scanning phone)?
If it detects nudity, what kind of unwanted behavior might it exhibit then, report to legal guardians? Not the picture itself but even just that the device is being used for that.
I can see how this scanning+warning is more creepy than scanning+labeling cat pictures, even if the information screen tells you it was just used for this warning screen.
Do you use an Apple device? I can see why non-Apple users lack trust.
Apple would be eviscerated if they were doing more than they claimed.
Other devices makers are excused for poor behavior. Often with the tech-bro response that is some flavor of "install a custom OS, bro!"