Eventually I googled the problem, and got linked to some random non-Amazon site, that told me to go find the generic "Help" link, and dig through a couple screens until I found a link to a chat interface (basically a "nothing here is helping me" link), where a robot would help me. The process worked perfectly and easily once I got there, but there's no way I would have gotten there on my own.
I suspect some people, when confronted with a missing item, will try part of what I did and just give up and eat the cost, especially if it's a cheap item. So the internal metrics look good, but that's not telling the whole story.
Black Friday, I got charged for the item but nothing else changed about my tracking. A few days later, after a similar search, I found the help link and got a refund. To this day, I have no idea whether my item ever made it out of the warehouse.
Amazon doesn't provide any discoverable way to complain about this either so I'm sure their internal metrics look great.