If from a geometric perspective the non-halogens, non-noble gases have more empty spots in their valence shell, and the filling/exiting of any of the empty spots in the shell constitutes a chemical rxn, shouldn't non-halogens and non-noble-gases be more reactive? (AFAIK) Just from a probability perspective, the probability of hitting the empty spot in the electron shell which is crowded by 7 electrons already is just less likely when you can hit any of the >1 empty places in the shell of the electron accepting atom. I'm aware electrons are non-stagnant.
You are considering "a probability perspective" that may not be adequate for chemical binding. I think that it is energy what determines chemical binding.
First, what do you mean by reactivity? All kinetic data indicates the rate of a reaction depends on the collision probability of reactants with sufficient kinetic energy, and the energy difference between ground and activated state. The energy difference depends on a number of things but as a generalization it depends on the energy of the valence electron on whatever state it is in. The bond energies DO depend on the number of empty orbitals, but not in the way you think. If an electron from atom B pairs with an electron from atom A, it takes the energy of atom A in then region of atom A, and vice versa. If the space available to the electron in atom A is reduced, the energy is increased. The reason the halogens are so reactive is because an electron entering their valence shell gains more kinetic energy because the space available to it is reduced. (That the nuclear charge appears greater arises from the same reason, but is more complicated to explain.) That fluorine is the most reactive is because it is the smallest, and an electron entering its valence shell has the least room to move and is closer to the nucleus.
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