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.
Does anyone know the answer to this? I'm very curious. I actually wonder if it would be worse to report that you have video evidence of a thief, because they may no longer be liable (hey, we delivered it to where it had to go, rest is up to you) vs just saying 'it never got here'.
I can’t speak for everywhere but in the UK most places will send you a replacement if the item was left on a porch and then stolen rather than with your neighbors. That is considered a failure of the delivery company.
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.
You haven't taken receipt of the package by it being dumped on your doorstep. (I suppose with the exception of a delivery instruction 'leave on doorstep'...) While it may not be 'their fault', the choice of courier and their instructions is; it's also to some extent a cost of doing business.
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.
There's a lot of discretion, I think - it's a customer service issue primarily, but I generally haven't had to provide any evidence (but I imagine if I claimed some high percentage of all my orders from one merchant were stolen, they'd demand proof or ultimately refuse to accept my orders).