Thing is that the ideal might not be the golden ratio. Maybe we prefer pi/2 instead of (1 + sqrt(5)) / 2. Who's to say? Pi/2 is if anything -more- fundamental. It seems to be that we don't like things to look too square or too oblong, which limits us to the range of 4:3 through 7:3 as 'aesthetically acceptible'. phi just happens to be in the middle of this. So is pi/2, as noted previously.

You could test this, by showing people some rectangles and asking which ones they like -- 1.4:1, 1.5:1, 1.6:1, 1.7:1, 1.8:1, 1.9:1, etc.

One thing that's interesting is the rise of 8:5 screen dimensions over the old styles of 4:3 and 16:9. 8:5 is, coincidentally, right next to phi, and is in fact a convergent of its continued fraction. 8:5 includes 1280x800, 1440x900, and 1680x1050, 4:3 includes 640x480 and 1024x768, and 16:9 includes the oddball 1366x768. It could just be that the math is easier with 8 and 5, though, since their reciprocals both terminate.