Zip is also highly correlated with income which is correlated with giving a shit-ness, but I take the point.
To be more precise, the effect of education, as defined by something like school quality , is likely realized for some small fraction of students who can be affected by school quality. But of course the question is also about alternatives, if the choice is a good public school or a good private school it doesn't really matter. If its between a rural public school and home school, it probably doesn't. If it's a shitty public school vs a good private school, it probably does
The point made in a much more rigorous way here:
https://dash.harvard.edu/handle/1/30208853