I don't think the video evidence is meant to help the police (or, obviously, to deter the thieves), but it's useful for requesting a replacement from the shipper.
Further to that point, I haven’t even needed to provide evidence of stuff having been stolen. Which seems like a system ripe for abuse but it’s nice that it’s weighted in the customers favour for a change.
Thankfully I’ve not needed to complain about stolen stuff in a long while, partly because generally stuff is tossed over a fence or left with neighbors. But mostly because I now live in a quiet village so I don’t get the same kind of passing opportunists like I did when I lived on a busy school road.
That said, I seldom see or have stuff left outside in the UK - assuming no 'if out' instruction - the vast majority of the time it's a 'sorry we missed you' note or occasionally with a neighbour/over the wall.