I've seen similar suggestions, but it's ... probably not an especially useful conceptualisation.
The conceptualisation of elements is useful to us because physical characteristics of atoms are (mostly) stable over time, with atoms having distinctive masses, atomic numbers, and most importantly, electron shells. The latter account for most of what we consider to be "chemistry", along with some other effects, most notably the van der Waals force.
Neutron stars ... lack most of this. They're in constant flux, they (probably) don't have stable masses (if only due to constant accretion) or atomic numbers, they probably don't have anything resembling an electron shell, and in interactions with other objects any electromagnetic forces would probably be overwhelmed by gravity or, say, spin-induced magnetism. If a measure of a concept or model's usefulness is how much it explains behaviours, "neutron-star-as-element" doesn't buy you much.
Though there's possibly some truth or conceptual validity to it.
Questions are almost always worth asking, and there's at least some philosophical interest in this case. But from a practical perspective as a chemical phenomenon, not much use.
I subscribe strongly to a pragmatic approach to knowledge and understanding. That is, knowledge isn't so much true as it is useful, in that it provides a useful mental model of the world. There are cases where multiple truths are possible, as with wave-particle duality, or mass-energy. Either classification may be useful, that is, provide predictive, understanding, or manipulative power, depending on contexts and circumstances. Some of the classic philosophical paradoxes (Sorites, Ship of Thesus, falling tree in a forest) resolve at least somewhat under this view. What is often called "truth" I think of as "useful mental models". The distinction is that whilst both are grounded in observation and empiricism, "truth" is an absolute, whilst "usefulness" is a bit like evolutionary fitness: changing over time, dependent on circumstance, not entirely arbitrary, but also not perpetually fixed.
So, is a neutron star a gigantic nucleus? Yes, in a sense, in that it's primarily made of what we'd otherwise consider nuclear material. Does this give us useful insights on neutron star behavior above and beyond those given by gravitational, thermodynamic, and electromagnetic descriptions? No, not really, because the attendant characteristics and properties of much smaller nuclei (from atomic number 1 to the low 100s or so) simply don't apply. There's not much behaviour that is explained, predicted, or controlled by applying that knowledge.
A good question, and mostly beyond my pay grade. Almost certainly based on models rather than direct observation, though informed by the latter.
I'm struggling to find a strong source, but this page, by M. Coleman Miller at the University of Maryland, describes properties suggesting modelling over observation. Specifically it describes "the guts of a neutron star":
Even further down, you mainly have free neutrons, with a 5%-10% sprinkling of protons and electrons.
With an subsequent 'graph:
Yes, you may say, that's all very well for keeping nuclear theorists employed, but how can we possibly tell if it works out in reality? Well, believe it or not, these things may actually have an effect on the cooling history of the star and their spin behavior!
What follows is more description of theory with a few points based in what is directly observable, largely spin (via radio astronomy) and some temperature observations largely in X-ray observations, and the occasional gamma-ray burst.