Why aren't standard picture sizes proportional to each other?

Question

Example: a 4x6 isn't proportional to 5x7 and 5x7 isn't proportional to 8x10, etc.

Answer 1

It goes back to the late 1920's and the 1930's when color film first came out and 'black and white' pictures became easier to take than the early days of photography.
Kodak and Ansco film were the two BIG brands.
Contact prints from those films were small and very often enlarged.
A bunch of companies made cameras and there were quite a few film sizes. Contact printing and enlarging that variety of film sizes evolved into standardized enlargements such as 4x5, 5x7, 8x10, 9x12.
Enlargements were 'cropped' which means, either part of a side edge or part of a top edge were cropped off to make the feature of the picture fit those standard sizes.
Sometimes a customer would get something cropped out that they wanted in the picture. Then, the print shop might (or might not) print new pictures cropped as the customer wanted.
In other words, enlargements didn't need to fit the size of contact prints.