Yes you can, and legally in most states. The law accepts possible / probable future bad acts by the perp.
Quite frankly, I don't think you're any better than they are. Your willingness to kill over so little makes it hard for me to believe in fact that you're anything but the same side of a troubling coin, perhaps even worse as most robbers don't usually kill people unless they absolutely have to.
Not better just willing. Lots of citizens arrests are made here and VERY few result in shots fired, so your bloodlust theory is just uninformed speculation.