The thing is, the reasons given to engage in intervention (such as the drone strikes) should have justification that isn't paper thin. Saying "There are terrorists around here" is not a valid justification in any world. There is no logic in saying that, "If the Security Council won't authorize the action (which we have unilaterally deemed necessary) then we must take it upon ourselves." What on earth is the point of the Security Council if we're just going to roll over them whenever we feel like it? That simply isn't reasonable in any sense of the word. It's like giving the keys to the car to the UN and saying that they're fully in charge of the situation... and then when they won't let us take a joyride we beat them up and just take the keys anyway. It's completely empty. If our justification were actually sensible or even existent, they might be able to give us the OK, but because we've decided we need it, we're just taking it. Of course, this type of US exceptionalism is pretty much the norm so its not like it should surprise anyone. But the idea of it being an enforceable international policy is awful. By this logic Pakistan could say that they're justified to attack us on the basis that the Security Council won't permit "counter measures" to stop the drone attacks on their citizens. Since they're not the US though, they'd never be able to get away with half of what we do.
The problem is that there is no guarantee that the UN will ensure that an action is moral or just. Russia continually vetoes any action against Assad in Syria. On the other hand, the only reason that the Korean War happened is that the Soviet Union decided to boycott the UN. Let's not even discuss the issues in Kosovo or Rwanda wrt the UN. I suppose my point is that UN or NATO approval is not necessary nor sufficient for moral military action.
You're correct that it's not necessarily moral. However, having an actual, enforceable system in place does mean that at the very least there's some kind of rhyme or reason to what happens. As it stands there's nothing stopping anyone from doing whatever the hell they want and the UN effectively can't do a thing, even if it's against the geopolitical rules we (countries) all, ostensibly, agree to. When any non-justification gets through without so much as a sanction or a dirty look, the system is -- well, it's not even broken. It's just non-existent, and I'd rather live in a world where some law was preventing any country from doing anything at any time. You are philosophically correct, I want to stress that - I don't think that giving any organization the ability to decide what is and isn't allowed wholesale is inherently good. But I think it's better than letting world power governments get away with literal murder because of their power. I would consider that an outright failure of the organization to "protect individual human beings, not to protect those who abuse them."