Can you give me the reason why it is not attractive to form the genitive out of an uncountable noun? What is it about an uncountable noun that makes it less attractive or make it less popular in terms of its usage in the genitive form?
You are not asking an easy question. The 'apostrophe ess' form is called the Saxon genitive, which is derived from 'Old English', so it's a very old feature of the English language.
It indicates possession or close association. Perhaps it's easier to see/feel close association when you are talking about something you can count?