Before I start, I want to say that I know that the spirit of the rules is for narrative Inventory in many situations. I have been using the preferred method of handling inventory and items to try and avoid the players looting the blasters of the fallen NPCs, but in doing so I found that the players tended to have the working idea that they had anything that was convenient for the moment whenever they wanted it. I had to crack down on the incidental possessions because it was driving me crazy that they had a house full of stuff but a fanny pack worth of storage.
Does anyone currently, or have you in the past, run your game with 100% accountable Inventory except for what comes up in a scene for the expenditure of a Destiny Point? In a current EotE game I am running I have a copy of every player's equipment list/wealth and if it's not on my copy they don't have it. I even have them specify what is in their utility belt instead of just letting it be a bag of tricks. I felt like in earlier games the loose nature of the inventory was making the rarity system feel like a useless appendage, and the ability to keep the group hungry was sometimes hampered. I tried to get the group to be reasonable with their incidental items but it got to the point where I couldn't stand the Batman-level of handy item possession. I know it isn't Star Warsy, but one too many times the magic hat got invoked and I lost enthusiasm for narrative inventory.
Also I try and assign ownership to most things in the game large and small, so that the players are not simply using the world as a free for all dispensary of equipment and materials. If something is valuable then somebody probably owns it and taking it is probably going to be an illegal way of getting it (except in places where there is no law and order obviously).
I also have been focusing on Encumbrance. Several times they've attempted to steal things only to realize what a pain it was to carry those items away, or to have to watch out for the owner/security forces.
What are the pros and cons as you see it of doing things this way (other than player agency stuff cause the players are fine and nobody is pursuing legal action), and if you enjoy or are proficient in running this way what tips do you have?