This is a troubling situation that many of us have dealt with at some point. I can think of no sector of the economy where a merchant accepts a risk of performance for an insurance premium and then steadfastly refuses to make good on their responsibility, no matter what. It is clearly their business model, all of them. We all know how abused packages are by all shippers.
When I ship with Fedex/USP, always in original packaging or at in least double-boxed well-protected cartons, I always which I make a point of showing to the shipper, in an open box, that I have properly packaged content. I video the whole exchage to hear them say that it is properly protected for shipping and they then ought to accept any damage that might occur with the insurance premium, clearly cause by their handling of the package. This evidence is vital in pursuing your claim which might take a lot of time and effort, but it might compel them to settle with you.
The fact of the matter is that it is David against Goliath in these situations, but my experience is that you if you are vigorous in your pursuit of the claim, you will likely prevail. There ought to be a law against this routine refusal of shippers to take responsibility for the risk they took on with the insurance premium. Otherwise, why purchase the insurance, right?