At the highest level of abstraction...
You only have two ears...
Therefore perfect surround sound CAN be produced with only two channels of information.
And, yes, you ARE able to recognize sounds coming from above you, using only those two ears.
(If you've ever heard a really good binaural recording through good headphones then you know this to be true.)
The catches all come about when life, and rooms, and speakers become involved.
First of all, a perfect binaural recording is only perfect when your head is in one particular spot.
So, if you're listening to that perfect binaural recording, and you turn your head 30 degrees to the right, the whole orchestra you're listening to follows your head, and also swings 30 degrees to the right.
This is probably what you want when you're listening to music - but it's really odd if you're watching a movie and the sounds move around while the things on screen don't.
So you can reproduce perfect 3D sound with only two channels... but either you must avoid moving your head or the information in those two channels must ADAPT to your head position.
Apple is trying to do this with their new 3D thing...
And there is a gadget called The Smyth Realizer which does it with headphones...
It's really expensive, and there are reports of all sorts of issues and limitations, and of course you MUST use it with headphones, but it is said to work really well... (I've never heard it.)
Second, as you might expect, unless you're using headphones, there is NO POSSIBLE WAY to get SPECIFIC information to ONLY one ear or the other.
It is simply physically impossible for a loudspeaker to be perfectly directional, or to have perfectly controlled dispersion...
It is also physically impossible for any sort of room correction to prevent or cancel out all reflections and room interactions...
(This is NOT "something that could be done if only the software was finally good enough". It is PHYSICALLY IMPOSSIBLE. Hard stop; period; end.)
Here's what I see for the future (excluding a direct neural implant that bypasses your ears entirely)...
A system that would function along the lines of the Smyth Realizer...
Each listener would wear individual wireless headphones ear earbuds...
The master system would then track the position of each person's head and send them a binaural signal custom created from the original surround sound signal for their current head position...
(Note that such a system could combine earbuds with a separate physical subwoofer... which opens the door for really unobtrusive earbuds or headphones.)
It's either that, or we stop obsessing over accuracy, and settle for "a system that sounds really nice and is reasonably accurate".
"Accuracy" is another of those ridiculous audiophile notions that has no meaning in the real world unless you are a designer. If you are designing and building, say, an amplifier, then you care about measurements and accuracy of the electronics to try and achieve "input = output." If you are a user at home, you care that it sounds good to you and that the result reasonably recreates what your mind thinks "music" or "movie soundtrack" is supposed to sound like. Most users in their homes would not know true "accuracy" if it bit them in the behind, and many when presented with the sound of a perfectly accurate system do not like it.