I'm sorry,
but I must disagree with the generalization.
You
described "the very nature" of a typical recursion over a
list:
(1) deal
with the head, then
(2) deal
with everything else.
But lists
are not the only recursive structure. Infix-order processing
of a tree, for example, is more naturally described as:
(1) deal
with the left sub-tree (the first "everything else"),
(2) deal
with the parent (analogous to the head of a list),
(3) deal
with the right sub-tree (the second "everything else").
At the risk
of a spoiler...
.
.
.
.
One approach
to the Towers of Hanoi problem emerges nicely from thinking of
the moves as a tree.