The article is specifically addressing the US's status as a significant outlier WRT gun homicide. The article addresses your point that homicide represents only a fraction of total gun deaths.
I don't see a problem with "modernization". Constitutional documents should be living documents, tuned for clarity and for the times. Of course, such changes should not simply be a matter of passing a new bill. There should be significant political hurdles involved.
No "beginning" does not mean no "big bang", and "big bang" is a completely shite term to begin with. "God Particle", "Y-Chromosomal Adam", "Mitochondrial Eve" ... the boffins who think this shit up should be (metaphorically) shot.