Many thanks for your comments again, Professor Asghar!
The various models of the nucleus have a long history, going back to the 1930s, and I often refer to the Fermi-gas model, the shell model and the independent-particle model (IPM) collectively as the "gaseous-phase" models. As you note, in fact, their theoretical foundations are quite different. The Fermi-gas model was little more than an analogy with the gas contained within a fictitious boundary. The early shell model was constructed around the idea of a central potential well - in analogy with atomic structure, but of course without any central attracting object that could act as the central potential. The "central potential well" was assumed to be the net result of the many local, nucleon-nucleon interactions... an interesting idea, maybe, but purely hypothetical as a mechanism for binding nucleons together into a stable nucleus. Everyone understood and most textbooks acknowledged that the central potential well was a dubious ploy, but the shell model nonetheless had many theoretical successes.
As you have commented, the modern IPM utilizes a nuclear force. From the perspective of theoretical coherency, the use of a realistic short-range nuclear force is huge progress. Unfortunately, the modern IPM also requires a theoretical "trick" to make the model work. That is,the Pauli exclusion principle must be "enhanced" to maintain the "gaseous" phase that the short-range force, on its own, would not allow.
As connoisseurs of nuclear structure theory well know, the exclusion principle was first suggested by Weisskopf in 1950 as a possible mechanism to allow nucleons to move like the particles within a gas under the influence of the shell model's (fictitious) central potential well. He argued that "exclusion" might justify the shell model's underlying theoretical assumptions, but the exclusion principle has been, over the decades, gradually "enhanced". Instead of a simple statement that "no two fermions can have the same set of quantum numbers" (which was Pauli's original formulation of "exclusion"), the exclusion effects have been referred to as "Pauli blocking" and even as the "Pauli force". It is not clear, dynamically, what that "force" is (and others have complained about this reification of Pauli exclusion into a force of nature), but without the "blocking" of the powerful short-range nuclear force effects, the nucleus would condense into a high-density liquid or solid.
That is of course precisely what the fcc lattice version of the IPM predicts. If it is assumed that, without a Pauli "force", nucleons condense to a solid of nucleons (a close-packed, antiferromagnetic face-centered-cubic lattice with alternating proton and neutron layers), then it is easily shown that the properties of that particular lattice neatly reproduce all of the quantum number properties of the nucleus - for which the IPM is justly famous.
So, I return again to the seemingly paradoxical position that I have stated before: I fully agree with Prof. Asghar that the "shell model" (IPM) has been wildly successful over many decades. Those successes cannot be ignored, but I maintain that the gaseousness of the shell model (and the implied nucleon orbiting and the Pauli blocking of the inevitable collisions of orbiting nucleons) is not necessary to explain the IPM quantal regularities, insofar as the lattice contains the same regularities. From a conventional point of view, it may seem unfair for the "new kid in town" - the fcc lattice model - to stake a claim for the shell model's theoretical successes, but I maintain that it is simply uncertain which model is mimicking the other!
Without the quantum mechanical properties (the independent-particle states) of the IPM, the extensive and rigorous data on thousands upon thousands of nuclear isotopes become incoherent, so that the known shells and subshells of the IPM - and the occupancies of nucleons in those shells and subshells under the influence of the exclusion principle - appear to be essential. But I think that factors of serendipity and chance, more than logical necessity, led to the overwhelming predominance of the gaseous-phase shell model and it becoming the central paradigm of nuclear structure physics, while Wigner's original proposal of the lattice structure of the nucleus in 1936 was seen simply as a mathematical analog (and Everling's suggestion of the lattice as a coherent nuclear model in 1958, and Lezuo's solid-phase formulation in 1974, and subsequent developments in the same direction have been ignored).
There are undoubtedly other criteria that can distinguish between the solid-phase and the gaseous-phase models, but it appears that neither model can assert that the well-established independent-particle systematics of the nucleus unambiguously supports one model over the other.
