People like to requote versions of this.

But all airlines (and usually their ground handling agents who also work for all the other airlines) lose bags all the time. And of course it's always a pain in the butt.

In fairness to QR in this case though, it's difficult for them to settle a formal and documented Montreal Convention claim made 21 days after travel for the depreciated contents of a bag that appears to be formally lost (as they themselves say they will on their website) when such a properly documented claim does not appear to have been made.

Baggage services offered a cash gesture when it was delayed. Claiming later for a total loss requires a separate claim to Customer Services, as QR and even the US DoT indicate.

Perhaps there's a reason the OP prefers to avoid the scrutiny of making such a claim, they sound like they may be serially litigious. But I can't imagine a claim to QR requires any less detail and documentation than claiming through insurance or DoT or court. In my experience QR are quick to deal with legitimate and properly documented claims when something goes wrong. The OP is choosing not to follow the established procedure.

It's probably not unreasonable to expect the DoT or a court or a travel insurer to reject a claim made for the equivalent of the Montreal Convention compensation limits if no such documented claim has first been made with the airline

Like I said, best of luck...