I had an experience with AA baggage at SFO that was ultimately resolved satisfactorily, but had some speed bumps along the way.
I had a steel-framed bag where the steel was bent enough that several welds had broken (in addition to the wheels being ripped off, the cover being ripped, an interior wooden panel being broken in half, etc.). It was sort of funny--in fact, I'd seen the baggage loaders laughing when they saw it.
At SFO, AA agreed compensation was appropriate. We agreed on a mix of miles and a limit on what they'd pay for a new bag (together, they approximated the cost of a new bag). However, AA wanted to take the old bag. This was a problem, since they didn't have a substitute and I didn't want to carry a bunch of loose items home on BART with my other luggage. Finally, they let me hold onto the broken bag so I could get home.
Also, AA wouldn't cut a check until I provided proof of getting a new bag. No problem--could I mail them the receipt? No. I had to return in person and show them the new bag. Okay--except the right people were never available when I went back to SFO baggage with my new bag to get the check.
Finally, the right person is available, but now it is maybe 60 days later. "You had to come back within 30 days," he tells me. This is the first I've heard of this requirement, which is surprising to me, because you'd think they would have mentioned it on one of the occasions when I was there in person, speaking with them. In any event, I'd been back within 30 days--luckily, one of his co-workers remembered me from a few of my visits, and they cut the check.
I could see where most folks would give up on getting compensation--and my discussions led me to believe that a non-elite flyer would have received nothing, anyway. The whole process seemed arbitrary.