Perhaps you aren't familiar with how large a sample is valid for a given degree of confidence.
That would only be applicable if the sampling areas tended to have measurable proportionality results, and there were at least some higher degree of similarities between the areas sampled.
If all jurisdictions had some degree of relative proportionality, and all of the same jurisdictions were participating at the same rates each year, then perhaps something could be inferred.
For instance if
If Township A has always reported 80%+ of their their car break-ins, and continues to report 80%+ of their crimes
If City B used to report 80%+ of their car break-ins, and when they did, it could be observed that for every 1 in Township A, there were 3 in City B. (establishing a high-confidence link in proportionality)
Even if City B stops reporting a high percentage of their crimes, there are certain inferences that could be made about B based on what we see happening in A using historical trends.
That doesn't exist for this scenario.
1) Crime rates in the burbs are somewhat disjointed from crime rates in the high population density cities
2) Crime data reporting in NY has been something of a scatterplot (One year precinct A reports 20%, the next year 5%...precinct B does 8% one year, 15% the next, etc...)
To use a medical comparison, it'd be like trying to make inferences about the impacts of higher dosages about "Medication XYZ"
If researchers reported 80% of their results for 18-29 year olds
Only reported 15% of their results for 61 year olds
Only 18% of their results for 62 year olds
...and had a 6 month backlog for reporting the results for 63-69 year olds
It'd be very difficult (with any degree of confidence) to take the 18-29 data and use that to make inferences about the impact on 60-69 year olds.
A) because we know there are differences in how well different medicines are "well-tolerated" by age group
B) not enough data has reported about the latter to try to establish a proportionality/trend link between the two.
@sfs is something of a stats guru, I would be interested in getting their take on the matter.
All of this part aside, with regards to why the public has the perception that there's more crime, what I mentioned in my previous post is still applicable. Despite murders and rapes dropping by 11%, those happen far more infrequently than assaults and larceny. So a 6% increase in assaults/larceny is going to be more noticeable to the populace than an 11% decrease in the aforementioned more serious crimes.
It'd be like if there were a 10% decrease in traffic fatalities, but a 10% increase in fender benders... The roads are "safer" in terms of fewer people dying, however, society going to observe an increase in non-fatal accidents since those happen to far more people.