My pleasure, Mitra. As you notice, there are certain set phrases that require 'of': "degrees of freedom", not "freedom degrees"; "soup of the day", not "the day's soup" (but it can be "today's soup"); "rite of passage" is more common than "passage rite". I think this is because ambiguity arises: Can one get a college degree in "freedom"? Which day's soup? Passage through what?
As for using other prepositions instead of 'of', learning prepositions is tricky in most any language, but it can offer a lot of expressiveness. Now if only I can practice what I preach.