To be fair, I will presume that YOU intend to eliminate ALL those with any negative view of the US- Otherwise, they would still be a threat. "the only way to reduce the possibility of deaths due to nuclear attack from such groups is to work toward eliminating the injustices that result in the existence of terrorist groups in the first place."
Do you think that we can remove ALL the perceived injustices in the world? How will you deal with opposing sides- Israel settlers Vs Palestinian terrorists- YOU claim you can get EVERYONE to agree the US is doing the right thing at all times? If not, YOU have no right to demand that a missile defense be 100% effective before it is worthwhile.