Bins and barrels are actually the intended method for improving space density.
Says who? Both of these have uses still in a quantum stockpile world, which could instead be the main reasons they are in the game. Barrels store liquids, which packed stockpiles don't do. And bins allow huge numbers of items to be hauled all at once (such as to the trader), which packed stockpiles don't do. On top of this, having two ways of doing something does not prove anything about one of them being "cheating." I can kill a goblin with a sword or a crossbow bolt, is either of those cheating?
If you want to establish those stockpiles as "cheating" you additionally still need to explain why Toady put minecart dumping into the game, for instance, when nearly 100% of the time, it leads to quantum stockpiling, and virtually cannot be used any other way. Are you suggesting he is too stupid and lazy to have tested his new feature even one single time, or that he just didn't notice that it was piling in one tile? I'm not seeing any other justification for that feature being "cheating" when used in the only way it can be used...
Item volume isn't fully implemented yet
Yes it is. Volume is already used all the time and there are already algorithms in place for determining how many things fit in a given volume. Like you say, for bins and also for barrels and every other container in the game. Chests, backpacks, cabinets, etc. As well as the "cluttered" flag in workshops.
Also, you're simply wrong about the seeds, etc. Seeds currently take up 0.15% the volume of a statue. Seeds are 10, statues are 6,000. Socks are variable based on the race who made them's foot size, but are for dwarves very small compared to statues.
It's actually rather confusing whether these are the volumes in cm^3, or 10x these, it seems to use different units in different applications in the game. From common sense I think it's actually 10x those, because then a statue would be the same size as a dwarf (60,000) which makes sense. If not, it should be, whatever. 10 minute change at worst to add zome zeroes to stuff.
So if a tile is about 1.5x1.5x3 meters, according to Toady somewhere I think, then it has 6,750,000 volume units (cm^3) in it. If statues were amorphous solids that could fit with zero airspace, you could fit 100 of them in that space (same goes for dwarves themselves). If we want to take into consideration that statues are shapes with air amongst them and don't stack on top of each other, then divide that by 10, let's say, and you could fit about 10 statues in a tile.
Or 600 seeds. Both seem quite reasonable, actually. I'd be totally fine with something like that but no quantum stockpiles at all. That is realistic.
And if you build shelves (material-requiring stockpile upgrade), then you can fit twice as much per tile, say.