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...
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One approach to the Towers of Hanoi problem emerges nicely from thinking of the moves as a tree.