I suspect a survey of residents, asking questions like, "have you had anything stolen that you did not file a police report about?", would reveal relative urban versus suburban or rural propensity-to-report trends here better than official crime stats – but I don't know of such a data series.
I've never had to file a police report for theft in NYC (where I've lived for 20+ years), because I've never had anything stolen from me. Unless you count the kid who, in third grade, stole my Pokemon cartridge. But the response to that involved schoolyard justice.
But "independent adult" also doesn't mean much. I was riding the subway alone by the time I was 7 or 8, and didn't have anything resembling a curfew.
In small towns and cities all around the world, people don't report crimes for a variety of reasons. It's not clear why that would be more true in NYC than elsewhere.
If you were talking about petty theft, I'd agree with you, but for the most part, burglaries are nearly always reported.
As a poster above you mentioned, why report a crime if you know nothing will be done.