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The issue with the toy model is that an additional electric charge is added to the system without also subtracting this charge from the fixed negative charges representing the electron shell, and this negative charge does not interact with the electron shell points. Naturally this would increase the binding of the system as it introduces a purely positive attraction. In reality, the monopole shift reduces the binding energy of the system because the probabilistic superposition of electron and nucleus on the same position reduces the Coulomb attraction between the electron shell and the nucleus.
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