The biggest problem with this line of thinking is that chemical reactions rarely originate from a point of lone, neutral atoms. Sure, lone neutral atoms (except noble gasses) are incredibly reactive: so reactive that any differences in reactivity between them based on valence electron configuration are essentially meaningless as a practical matter. Maybe in outer space or the upper atmosphere* this might make a difference, but in virtually every practical, realistic environment, atoms are already contained in molecules, and they have filled valence shells.
Also, it is worth pointing out that "reactivity" is not a defined physical property. We may use it loosely to refer to certain substances that are unstable, or more likely to undergo reactions in a general sense, but that's more of a gut feeling than anything that can be measured or quantified. If you have two different substances, there no real way to objectively define one as being absolutely more reactive than another. Whether or not a substance reacts with something else depends a lot on what the "something else" is, as well as what the conditions are in which they find themselves. Distinguishing between thermodynamics and kinetics is also an important consideration.