I actually like the moral agonizing, because it shows that Cap is not a hypocrite.
I'm sick to death of mass-murdering, torture-happy villains who are always spared by the heroes, even at the cost of endangering countless innocents, because "they are still human! You can't kill a human being!" While apparently it's perfectly A-ok to kill far less despicable and dangerous villains who just happen not to be human. I loathe the "What Measure Is A Non Human" trope.
So, if Cap is going to do everything he can to avoid killing, say, Kang the Conqueror, then I appreciate that he has the coherence to treat non-human villains the same way.