I thought it was used because 7-bit ASCII had only 128 code points in which to fit all teletype controls, letters, numbers, and punctuation marks and symbols. They had to use each code point efficiently, and the ASCII double quote can be used as open quotes, close quotes, seconds, inches ... they also needed to support some European alphabets and therefore some punctuation marks, such as the single quote, double as accents when overtyped (using teletype control code points) on a letter.