That may be true, but even models can have a closer or less close relationship to the thing they model and modeling 3D orbits around a central nucleus is quite hard in a rectangular mapping, the spiral (even if this one may be flawed) seems to show more clearly that the space in orbits further out will accommodate more electrons.
What do you mean by "modeling 3D orbits"? Because that's not what the periodic table is doing. It's telling you which quantum numbers are in use. The rectangle is extremely good at that (with a couple minor simplifications). The problem with the spiral is that it will have the same discontinuities as the rectangle, because each angular momentum number has two more magnetic quantum numbers than the previous.
Or, in other words, the disadvantage of putting more space farther out is that you lose the most important property of the periodic table, which is the groups.
2n^2, that the underlying reason for that equation is a quantum effect is not required for the basic understanding that 'further out' means 'more room'. That in the end the equations are about energy levels rather than space does not matter when you're trying to remember what the periodic table looks like, it's a useful mental construct, even if it is fundamentally in-accurate.