Fwiw, without going into too great a detail, since 2008 I have been party to 3 USPS claims, all which were paid out. Granted, 2 were within a year of each other and in 2008, but the third was last year. The process was essentially the same on all 3.
None were for knives, and I was the buyer on all 3 (and I had to help the sellers navigate the process). 2 of 3 were eBay purchases; one was a used motherboard which was damaged beyond use/repair, and the other (recent one) was some electronic parts which went completely MIA midway through the system. The other one was a nice digital camera I had my sister-in-law purchase for me in another state. She stupidly packed it up in the PO lobby, in plain view of everyone. It never scanned out of the PO after she handed the box to the clerk. Thankfully she had an acceptance receipt. After the investigation, an employee was caught having stolen it, and claimed to have sold it. Said employee was obviously let go.
Anyway, the process wasn't difficult, but each was lengthy and required some paperwork. I just had to be persistent in checking in on things, and provided any proof that was asked for. So long as you have some kind of proof of purchase, you should be ok. Unfortunately though, YMMV. Porch piracy has become a real problem too, and you're pretty SOL there.