You clearly wanted the item with character A.

So when character B discovers it is in, do you not feel the temptation to log on character A and go grab it?

Even if character A always checks the mob, there's no guarantee you'd have played character A at the point in time you need to collect the item that character B saw. If character B hadn't seen the item, you might have carried on playing with B for longer. Long enough for someone else to grab that item.