Nor does it make sense for a monitor. I can't remember ever wanting to arrange a bunch of windows as a square, a smaller square, a smaller square, etc.
I must not want my wm to give me a geometric series of ever shrinking squares.
What else does it default to, if you open a new window?
Does/did make sense. European paper size (A*) are based on the golden section (so A0 Length == A1 Width and 1/2 surface A0 == surface A1 and so on).
Not quite. ISO 216 paper sizes are designed so that if you split them in half you get the same ratio (1:sqrt(2), or 1:1.414). The golden section is so that if you take a square out from one side, you get the same ratio (1:1.618).