Because ZKPs aren't the whole system.
If it allows regular checking (and they all basically have to), I can determine someone's exact birth date when they become an adult. If a system allows me specifying an age to check (as many do), then I can determine anyone's birth date.
Further the vast majority of people do not understand ZKPs. If some random website asks them to go verify their age by installing software or going to a website that requires them to upload an ID, a good percentage will simply balk. The fear of lack of privacy, regardless of actual privacy, creates a major chilling effect on speech.
The truly galling part is that all of this nonsense only exists because parents won't spend a couple minutes setting up parental control software. For goodness sake, it takes 30 seconds to turn on a filter that blocks all porn on the screen on an iPhone. I have little doubt that if governments required it - or simply paid for it, they could get apple/microsoft/google/etc to modify their parental control software to detect social media as well.