Mainstream science can easily explain it due to gravity providing a downwards force which acts on the balls/air and is countered by an upwards force from the balls/air below due to them begin compressed.
Clearly not.
That isn't clear at all.
What is clear is that your model is pure nonsense and you are unable to demonstrate a single issue with the explanations and model provided by mainstream science.
This is just yet another example of it. You have been asked to provide an explanation of how your air stacks (to then get onto why things fall) and you continually deflect. You claim a diagram that just shows air stacking somehow magically explains how it stacks. You repeatedly appeal to that diagram. And then you appeal to an analogy which relies upon things falling. Then when this is pointed out and a simplified explanation of why this occurs according to reality (mainstream science), you just dismiss it as "clearly not".
Once more, what is abundantly clear is that your model is incapable of explaining anything, while mainstream science can easily explain so many things, including why air "stacks".
If you want to disagree, in any way even remotely resembling an honest and rational attempt at disagreement, you need to provide an actual explanation as to why/how the air stacks in your model and provide a justification for why the mainstream explanation is wrong.
That means an actual explanation, not just a diagram showing it stacking (or other baseless assertion), not just an analogy that appeals to things falling, but an actual explanation of what magic causes air to stack in the absence of any force making things fall.
That also means not just dismissing mainstream science but actually clearly explaining why you think it is wrong.
Once more, with mainstream science, that observation is trivial.
Gravity acts on all objects near Earth to pull them towards the centre of mass of Earth. (If you wan to reject gravity you can replace it with whatever nonsense you want to use to explain why things fall).
This explains both why things fall and the directionality, and why it is proportional to mass.
Now that we have things falling, we can consider why they sponges below are compressed.
There is a force acting on all the sponges to pull them down.
Consider the sponges on the top (the 1st layer). They are being pulled down with a force of 1 U (unit).
They fall, and then hit the sponges below (the 2nd layer). They try to push the 2nd layer down which causes (as explained below) the 2nd layer to push up with a force of 1 U to cause no net force on the 1st layer.
Now consider the 2nd layer.
It has gravity pulling it down with a force of 1 U.
It also has the 1st layer pushing it down with a force of 1 U, meaning there is a total force of 2 U pushing it down.
It tries to push the 3rd layer down, which causes it to push up with a force of 2 U.
That means this layer has a force acting on the top and bottom to compress it. This compression, akin to springs, results in a force acting outwards to stop the compression. It is this force acting outwards that transfers the force through the layer, transferring the 1 U of force from the top to the bottom, and the reactionary force from the bottom to the top.
Now consider the kth layer.
It has gravity pulling it down with a force of 1 U.
It also has the k-1th layer pushing it down with a force of k-1 U, meaning there is a total force of k U pushing it down.
It tries to push the k+1th layer down, which causes it to push up with a force of k U.
That means this layer has a force acting on the top and bottom to compress it. This compression, akin to springs, results in a force acting outwards to stop the compression. It is this force acting outwards that transfers the force through the layer, transferring the k-1 U of force from the top to the bottom, and the reactionary force from the bottom to the top.
This continues to the nth layer.
The only difference is that the nth layer is on the ground, and thus it is the ground pushing up to keep the entire stack up.
The same kind of argument applies to air and other fluids. Except instead of layers of sponges, you have layers of molecules, and as it acts hydro-statically, it is based upon pressure not just force, and with air, as it is compressed, each layer get thinner, such that at ground level the layers of air are much thinner than much higher up, corresponding to an increased density and pressure.
See how this falling down explains why there is compression.
But you can't use any of that explanation.
That is because you are claiming this stacking is what causes things to fall.
Without that force causing things to fall, there is no reason for the air to stack.
So again, mainstream science can explain it, your nonsense can't.