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Full Idea
Each proposed revision of set theory is unnatural, because the natural scheme is the unrestricted one that the antinomies discredit.
Gist of Idea
The set scheme discredited by paradoxes is actually the most natural one
Source
Willard Quine (The Ways of Paradox [1961], p.16)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.16
A Reaction
You can either takes this free-far-all version of set theory, and gradually restrain it for each specific problem, or start from scratch and build up in safe steps. The latter is (I think) the 'iterated' approach.