Yeah, I would guess any issues with bins also exist with barrels and pots, it's just that you use a lot more bins than you use barrels, so you see it more with bins.
I would also guess the reason stockpiles won't do anything with items in bins is that otherwise your haulers would spend half their time moving stuff around between bins. I think there just needs to be an exception to this when the bin containing stockpile is set to give to another stockpile, so that items in bins can be properly distributed into separate stockpiles.
(For an example of what I'm talking about, create an ammo stockpile that takes bins. Make bolts and bins. Once you have a bin with bolts in it in that stockpile, create a second ammo stockpile, with no bins allowed. Set the first stockpile to give to the second stockpile. Observe as no bolts are taken from bins and moved to the second stockpile.
Now disable bolts in your first ammo stockpile. Now you have a stockpile full of bins full of bolts, which it is not set to accept, while you have another stockpile happy to take the bolts, just no bins. Again, observe as no bolts are moved from the stockpile that does not allow them to the stockpile that does.
Now go ahead and just delete the first stockpile entirely. You now have bins full of bolts just sitting on the floor. You have a stockpile that wants those bolts, but not the bins. Again, observe as the bins sit on the floor with no bolts being moved to the appropriate stockpile.)
The only way to get those bolts out is for your bolt users to take them out, or for you to dump them.