If something akin to this exists then ignore my idea!
If it doesn't, then indeed I think it would be cool with some safeguards put in place. For instance:
(1) Items aren't all accessible. You have to literally dive a bit in the trashbin to check out what's in there. This, to simulate that this is a crowded city. PERCEPTION + what ever else nets you results, and maybe even you can find for something specific like the markets do. This will not let you immediately take everything from a trash bin, but you'll have to do some serious diving if you want to get the valuables. Toss in some worthless items that randomly spawn to account for vnpc trash.
(2) Items get progressively 'eliminated' from the trash bin's internal database. The more valuable an item is, the faster it gets flushed. Crowded trash bins also get flushed super fast. Anything too valuable maybe should eventually have a chance of ending in the markets to complete the circle. That way if you trash something super valuable, it shouldn't stay more than a few hours there.
(A) I believe interlocking systems always create emergent narrative. Sindome is obviously full of this stuff. Interlocking commands such as TRASH with an in-game mechanic and making you have to consider where you trash sensitive stuff (papers or what ever, e-notes) is obviously important.
(B) Nothing 'disappears' per say, but it isn't exactly traceable. Imagine you murder someone with super recognizable clothes. You toss the clothes in their trash bin and if someone comes to search the trash bin of their apt. floor in the coming one or two days, they might find them. If you want to trash stuff securely, you should figure out a smarter way. Maybe trash it at your gang / group / clan / corporation's HQ where only a member of it would need to snitch it out.
(C) New avenues of jobs appear. Fixers or beggars can literally dive through dumpsters, get codedly dirty, but probably find half-eaten food or what ever.
As a note, trash bin diving should probably tire you out or have some other creative way for staff to make sure someone doesn't just loot every single trash bin.
But yeah, that's the downpour of my idea.