I am pretty sure all mail is scanned (outer envelope) in the US (and I suspect in most countries) and the record is kept. So the police can tell after the fact what was sent to whom from which post office / collection point. I assume all it takes is a bit of CCTV to fully identify the sender.

There is no CCTV monitering a USPS drop box far from a post office. You could also address the package to your neighbor then take it off their porch after you see the USPS truck make their rounds. Or address it to a derelict property where you know no one will be home. Its trivial to mail things.