Unfortunately, it is common for those with power to see the data as a stick they can be beaten with rather than as a tool to do better.
Of course, an example of the negative potential also comes to mind: recently we got proof of extreme gerrymandering done using racial data. Obviously that isn't to suggest that data shouldn't exist, but more to underline your last point: fundamentally it can only be beneficial if people come to it in good faith.
Last I checked they were happily singing out about the data because legal gun owners shoot statistically nobody and military style arms kill statistically nobody compared to career criminals with boring old handguns (who mostly kill each other because they can't rely on the courts to mediate their disputes).
Fundamentally trying to insulate data collection from those with invested with the status-quo (in all situations) would be sensible.
Why couldn’t there be an SEC-type entity that requires periodic public filings from police departments or hospitals?
I doubt it. People have crunched the data that we do have and found that it doesn't support the popular narrative - and been fired from their jobs just for crunching the numbers.