Yes, if the people and governments were less emotional, we could probably avoid lots of deaths. However, let's not forget this isn't a matter where you can have only one thing. Researchers can improve cancer tratament while mechanic, civil and traffic engineers can reduce accidents. I'm not sure who's more qualified to reduce shootings, but we should also look into that.
Car accident fatalities per year according to this article[1]: 30000 (500+ per week) .
Low end estimates of flu deaths per season [2]: 3000
These latter two are not anything you would worry about significantly (they are not particularly likely to kill you). Why should I care about being killed in a mass shooting?
[1] http://www.iihs.org/iihs/topics/t/general-statistics/fatalit...
[2] http://www.cdc.gov/flu/about/disease/us_flu-related_deaths.h...