= Solution
The original table gives the dimensionless <branching fractions>
$$
B(\pi^0\to e^+e^+e^-e^-)=(3.34\pm0.16)\times10^{-5},
\qquad
B(\pi^0\to e^+e^-)=(6.46\pm0.33)\times10^{-8}.
$$
Thus the four-lepton channel is about $517$ times as frequent, despite its smaller available <phase space>.
The dominant neutral-<pion> interaction is with two <photons>. In <double Dalitz decay>, both are virtual and convert to separate <Electron>-<Positron> pairs:
$$
\pi^0\to\gamma^*\gamma^*\to(e^+e^-)(e^+e^-).
$$
This requires two electromagnetic conversions but does not force the whole final state into a helicity-suppressed two-fermion configuration. The two virtual <photons> and four final <leptons> allow the necessary <angular momentum> correlations.
For the two-lepton mode, a single virtual <photon> cannot mediate a $0^{-+}$ <pion> into $e^+e^-$: the electromagnetic vector current has the wrong quantum numbers. The leading electromagnetic mechanism involves two virtual <photons> attached to the same lepton line, with a loop integration. The resulting pseudoscalar two-lepton amplitude vanishes as $m_e\to0$, so its <decay width> has an additional <helicity suppression> factor proportional to $m_e^2/m_\pi^2$.
Both channels involve extra electromagnetic couplings relative to $\pi^0\to\gamma\gamma$. The crucial distinction is the extra leptonic loop and <helicity suppression> of the two-lepton channel; counting final particles or couplings alone misses it. The pion-two-photon interaction itself already contains strong-interaction structure, so “extra loop” here compares the diagrams after representing that common interaction by an effective $\pi^0\gamma\gamma$ vertex.
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