Is it possible to establish a model to describe neutrons as electrons and protons bound by the coulomb force? what disadvantages would it have?
There was a time when something like this was considered. A time when we knew of the electron and proton but not the neutron. To explain the atomic mass of an atom such as carbon, we supposed that there were 12 protons in its nucleus. So 12 electrons to balance it: 6 orbiting and 6 in the nucleus. I was reminded of this recently when browsing an old book on electronics, it said that carbon had 12 protons which was a surprise. Look up "nuclear electons" to find more on the subject.
Short Answer: It would be practically not feasible for such a nucleus to forms Why? Because as soon a proton and electron come together, they form a 'Hydrogen Atom', and hence more protons and electrons coming together will just make more and more Hydrogen atoms instead of any kind of nucleus.
Proton-proton repulsion will not be balanced by the coulomb force (between electron and proton). The model of the atom in such a case would be quite unstable, because the orbiting electrons would feel repulsion by the electrons in the nucleus and hence they will not bind to the nucleus strongly.
The nucleus you described above will be unstable itself because the short-ranged nuclear forces do not act on electrons. The coulomb force is about $10^2$ times weaker than the short-ranged nuclear forces (which are the binding force between protons). The electrons are the underlying factor in all chemical reactions, if electrons are considered to be inside the nucleus then every chemical reaction would require disintegration of the nucleus.
All the photoelectric phenomena we see in nature would be rendered unexplainable, because emission of electrons (which we observe during photo-electric effect) would essentially mean disintegration of the nucleus. The amount of energy required for that cannot be supplied by simple light ray photons.
In short almost all of the phenomena at the atomic level will become unfeasible.