The issue with this system is that anyone who loses their items would most likely hunt down the thief and kill him through meta-gaming. There is a reason when people RP'ly grief, GM's do not give out names. It leads to aggressive meta-gaming. However, if your character has items stolen from them, are you RP'ing it at all? No. You just want your items back. Otherwise you would go out to the bar, have a hissy fit, punch your wife, cry and then go get more items IC'ly. Nothing is stopping you from doing that, or roleplaying any form of anger, which actually will develop your story.
TL;DR - This system just encourages meta-gaming. You can RP without knowing who stole your items.