[Note also that the diagonals of the double square do not form the same ratio as the vesica. In the double square, the 1: 2 ratio is between the two short sides of the triangle, while the rhombus formed by the vesica has the short side being half the hypotenuse.]
Being a two dimensional figure, the square, the first measureable surface, is appropriate for the floor, while it's cousin the cube is appropriate for 3D space. Note the squares and rectangles in the image below, which mirrors those in the cathedral plan above.