Pauli Unhappy with his Exclusion Principle

A corner stone of standard Quantum Mechanics stdQM is the Pauli Exclusion Principle PEP stated by Pauli himself above. Pauli was awarded the 1945 Nobel Prize in Physics for the 

• discovery of the Exclusion Principle, also called the Pauli Principle.

In his Nobel Lecture Pauli recalls the basic problem he resolved by PEP:

• The series of whole numbers 2, 8, 18, 32... giving the lengths of the periods in the natural system of chemical elements, was zealously discussed in Munich, including the remark of the Swedish physicist, Rydberg, that these numbers are of the simple form $2*n^2$ for $n=1,2,3...$.
• The question, as to why all electrons for an atom in its ground state were not bound in the innermost shell, had already been emphasized by Bohr as a fundamental problem.

But Pauli did not believe that PEP was a scientifically convincing resolution: 

• Already in my original paper I stressed the circumstance that I was unable to give a logical reason for the exclusion principle or to deduce it from more general assumptions. 
• I had always the feeling and I still have it today, that this is a deficiency.

Pauli would probably say the same today: PEP is a mystery appearing as an ad hoc explanation of the fact that electrons in atoms organise into shells according to $2*n^2$ for $n=1,2,3...$ and so form the periodic table. The factor 2 would then be an expression of the 2-valuedness of spin. 

RealQM presents a different model of an atom where electrons appear as non-overlapping charge densities  which occupy a certain volume of space and the shell system of the periodic table resolves an energy minimisation packing problem. The 2 electrons of a Helium atom are in RealQM separated by a plane which gives the 2-valuedness a direct geometric meaning, which is passed on to atoms with more electrons. In RealQM there is no need of a PEP. This would have made Pauli happy and maybe another Nobel Prize.  

Pauli and Bohr eagerly studying physics of a spinning top.