Ok, see, this is how geeky I am. I research. OED lists the following:
Probable source of "easy as pie":
The US magazine Sporting Life, May 1886: "As for stealing second and third, it's like eating pie."
"Piece of cake" I know for a fact comes from an Ogden Nash poem from the late 1800s, cause I remember studying it in school, but I'll have to go Google it and find it for you.
"Soup to nuts" is obviously a reference from beginning to end - back from when a formal meal began with a soup course and ended with a nut/fruit/cheese course when the gentlemen retired to sip brandy and smoke cigars.
[History and Language Geek, present and accounted for.
]
As to why - I think that food is a common denominator for everyone. Almost everyone understands or can relate to a food reference, because we all eat. So I think it's natural that these statements would evolve based on our everyday life.
.