That kind of redundancy is a linguistic artifact, not a deeply meaningful one.
It’s not the case that reaching the second level of abstraction necessarily results in enough flexibility to make the inductive step. As a counterexample, consider C macros, which only add one meta- because they are only expanded once. Lisp macros, on the other hand, are expanded until a fixed point is found. That’s why Lisp macros are Turing-complete while the C preprocessor is only a pushdown automaton.
A bit of disagreement with your last paragraph: The (Common) Lisp macro processor is Turing-complete trivially because it invokes a Turing-complete language along the way, not because of power inherent in its expansion strategy.
Common Lisp macro bodies are written in Common Lisp, i.e. written in a Turing-complete language — they would still be Turing-complete even if we wrote them in the subset Lisp-without-macros. The C preprocessor, on the other hand, does not invoke a Turing-complete language to compute a macro's expansion.
It’s not the case that reaching the second level of abstraction necessarily results in enough flexibility to make the inductive step. As a counterexample, consider C macros, which only add one meta- because they are only expanded once. Lisp macros, on the other hand, are expanded until a fixed point is found. That’s why Lisp macros are Turing-complete while the C preprocessor is only a pushdown automaton.