Cops will often gaslight victims of crimes in an attempt to not have to do paperwork. I witnessed a man attempt to steal a car while the owner was unloading supplies into his store (a pizza place in NYC). He failed to steal it only because he couldn't get it into gear(a manual transmission), and probably damaged the clutch a bit.
when the cops showed up, it was clear the cops did not want to write it up, and went as far to accuse the owner of lying(and actual phrase said by the cops: "how do we know you didn't say he could sit in your car?", and threatening him with making a false report, or assaulting the thief by holding him until the cops showed up if he pushed it.
Of course, there could be other reasons for not doing it. Maybe they're under pressure from their commander to not take crime reports so the crime rate appears lower in the neighborhood than it actually is. But I assumed it was garden variety professional laziness.
But writing police reports is a nuts and bolts idea liable to introduce way worse problems than what it purports to solve.
Even if this did free up an officer's time, it's not guaranteed that would go to better policing. The department might see it as license to create heavier processes and more paperwork. These reporting requirements don't come out of nowhere, there are strong incentives to create visibility and accountability and they won't disappear if you make paperwork cheaper.