Leaving more space at the bottom is a technique used to center things 'optically' in a page (the same thing happens when you draw letters like 'H' 'B' 'S'), this is also explained in Gestalt inspired analysis (Arnheim, etc.)
Big side margins were used in manuscripts to allow for side notes, and sometimes in very dense typographic pages margins were filled with printed commentary (for example in religious books), like an heavy frame. Otherwise the big margins could be used for decoration (like in the 'medieval' revival of Morris's Kelmscott Press).
To save space in cheap or small books margins becomes smaller and every margin should be set equal. Therefore the big margins setting is used to convey a meaning of magnificence (for example in Italy, Adelphi uses this pattern of big margins in the expensive books – it is consistent with their 'corporate identity' – and small margins for the pocket version).
The idea of a 'rule' looks like a modern interpretation of a phenomenon (indeed it is often attributed to Tschichold), The so-called Villard diagram itself is a modern interpretation of a small drawing found in his notebook.
The idea of the golden ratio as a perfect proportion, imho, is also a modern one. My understanding of the Renaissance is that they were interested in integer ratios, like 'musical' ratios (1/2, 3/4, 4/3, etc.)
The idea of a 'rule' looks like a modern interpretation of a phenomenon (indeed it is often attributed to Tschichold), The so-called Villard diagram itself is a modern interpretation of a small drawing found in his notebook.
The idea of the golden ratio as a perfect proportion, imho, is also a modern one. My understanding of the Renaissance is that they were interested in integer ratios, like 'musical' ratios (1/2, 3/4, 4/3, etc.)
[sorry for my english]