Why is the original Pauling's theory of resonance that uses superposition of wavefunctions not used today?

I have recently studied superposition of states (also the famous Schrodinger's cat), measurement problem, decoherence & so on. I then read the resonance concept from Atkins' Physical Chemistry where it was written as:

It is the superposition of wavefunctions representing different electron distributions in the same nuclear framework. [...] A better description of a molecule of $\ce{HCl}$ is $\psi_\ce{HCl} = \psi_{\ce{H-Cl}} + \lambda\psi_{\ce{H^+} \ce{Cl^-}} $.

Thus this is the general wavefunction which is superposition of all the states. $\lambda$ is a numerical coefficient (can be found out by variation theorem) whose square predicts the probability of being in the ionic state when we inspect the molecule. Just like typical wavefunction-collapse after measurement! This is the original Pauli's theory of resonance. Unfortunately Atkins halts down here; after all it is physical chem-book! Nowhere have I found this approach to resonance; no organic chem book I possess: Morrison, Boyd; Solomons; R.K. Gupta ... They all say it is just the weighted average of all Lewis structures. No, it is not correct! As is said here:

This essay contains information that I have never found in any organic chemistry textbook. This can mean two things: the information is too difficult or you don't really need to know it. Maybe both are true .

[...] When Linus Pauling developed resonance theory, he defined "resonance" as the superposition of wave functions. Unfortunately, this detail has been lost in the intervening decades, and modern chemists incorrectly treat "resonance" as the superposition of Lewis structures (resonance forms)

[...]Suppose you have a molecular AB that is a resonance hybrid:

and you want to calculate the electron density on atom A.

The usual (wrong) prediction procedure. The usual procedure says, "combine what you see in each Lewis structure." In other words, combine the electron density (ED) on A in form IV with the electron density on A in form V:

$$ED_\text{wrong} \text{(hybrid)} = 1/2 [ED(IV) + ED(V)]$$

The much-ignored (correct) prediction procedure. You may recall that electron density (ED) is given by the square of the wave function (WF). If we want to know the electron density on A, we must look at the square of the wave function near A:

$$ED\text{(hybrid)} = WF\text{(hybrid)} ^2 \implies ED\text{(hybrid)} = ED_\text{wrong} \text{(hybrid)} + \boxed{WF(IV)WF(V)}$$

The final formula shows the discrepancy between the right answer, ED(hybrid), and the usual (wrong) answer, EDwrong. The correct formula includes WF(IV)WF(V). This term is called the "interaction density" or "overlap density," and is a product of two different wave functions. The interaction density affects the electron density everywhere in the molecule, and its appearance tells us that the electron density obtained by the "usual" procedure is wrong.

Electron density is just one of many properties that interest chemists, but all property predictions -- electron density, bond type, atom charge, dipole moment, geometry, energy, etc. -- have something in common with electron density prediction: the prediction procedure must start with WF(hybrid), and their answers always include interaction terms.

This is one of the great reasons why the modern concept of resonance is wrong; they don't take the "interaction term"!

So, why does only one book (which is not organic) contain the correct interpretation? Why do people follow the wrong version? Resonance is not at all the weighted average of Lewis structures; rather it is just a superposition of wavefunctions? So, why do most of the sources (people & book) advocate the wrong theory? Can anyone tell me which organic chem book still follows Pauling's original theory of resonance?

Added: In my quest to find the resources which still define Pauling's theory of resonance of wavefunctions, Feynman's Lectures, which I have just completed reading, is really worthy to be gold to be noted. Feynman completely describes the benzene molecule as the superposition of base states; it can be found in the CALTECH site.