It's YouTube and Instagram that are broken. The right to record is preserved. The ability (not right) to distribute is hampered by these organizations.
Why are you trying to diverge the attention spot here?
There's even a strong case for a third problem: copyright itself is a tool fundamentally one-sided and OP.
Three different things can all be true at the same time without detracting from each other.
The problem with focusing on just the police here is that there are any number of circumstances where copyrighted audio will be naturally occurring that the issue will require more than just getting the police to refrain from using the loophole.
I suspect the idea that they can play music in the background to prevent YouTube views is a misconception about how the system actually works.
Also, YouTube is not the internet or the world's preservation archive of video. It's a massive tv station from a massive ad company. I can't imagine there won't be a time where YouTube doesn't start deleting videos that are uploaded to their service just because they are taking up storage. So let's not give YouTube that power.
On one hand there is a personified "evil", which we are very good at handling mentally, dishing out imaginary punishments, righting their wrong etc. On the other hand there is a faceless corporate entity that not only scales massively in their "evil" but also in a way that is not quite intelligible to us right away. And our minds immediately flow to the more graspable object which is the cop, even though the cumulative harm of automated rent seeking is probably greater.
You think YouTube has any incentive in this? If it were up to YouTube they would just bring in rules that give creators ample flexibility while still making sure there's no infringement.