Well, last week I came back from Egypt (economy award) and noticed our Rimowa was seriously damaged in one corner. Walked over to the lost and found, the lady at the F/SEN counter typed up the PI report, gave me a card of a authorised repair shop, explained me the (new*) rules and send me on my way. Took 5-10 minutes. The family was tired and waiting for me at the belt at 10.30pm, so I didn't go into the intricacies of what you have to do for a stroller in a similar situation. But I saw a economy passenger being processed for a similar broken suitcase nearby and the agents were all friendly but particular. If the damage looked fresh and not like a preexisting condition the insurance LH Group has pays up without issue.

* The rules changed recently: no more on the spot replacement, no direct dealings with the repair shops either. OTOH the replacement value is nowadays a factor instead of the old residual value rule.