> it’s very difficult to think of a nonassociative situation.” If, instead of putting on socks then shoes, you first put your socks into your shoes, technically you should still then be able to put your feet into both and get the same result. “The parentheses feel artificial.”

I suggest the parenthesis are not artificial: they specify an order of operations. i.e. they specify the timing of operations.

Choosing a, b, c as things that change with time makes it easy to think of nonassociative examples:

(Crack open an egg) then (cook it) = (scrambled egg)

(Cook an egg) then (peel it) = (boiled egg)