You can't measure power without its effects just like you can't measure energy (at the very least, it will have to affect your measurement device), but you can often tell whether the effect was due to power or not. Sometimes -- like with the case of potential energy -- you might be able to deduce its existence once you've learned how it works for a while. But, you can often see powerful people fail (say, a billionaire dies in a plane crash, or loses all his money when the market crashes), and powerless people thrive (a homeless man wins the lottery). But power, like force in physics, is the main thing driving human interaction. It is certainly the only mechanism of any interesting social dynamics, but it is not trivial, as power -- like energy -- takes many forms.

So, to me, your question sounds a bit like, "how do we know when the planets in the solar system move by gravity, and when they move by something else?", to which the answer is that the planets almost always move by gravity, except very rarely, when, say, hit by a particularly large asteroid; how doe we know when that happens? We look. Same here, if a group has good outcomes and low power and vice versa -- while very rare (as power is at the core of the mechanism), you can either study the case carefully (which is what historians do), or compare it with power's known outcomes to see if it's one of those flukes. But, you'll say, I can isolate gravity and test it in a lab to make sure I'm certain this is how the planets move. Well, experiments like that are harder in the social sciences, but they are done quite regularly. Two very famous experiments in power are the Milgram experiment (testing authority power) and the Stanford prison experiment (testing authority power as well as its effect on those who have it). Many dictator games are experiments in other forms of power.

Besides, I don't see what exactly you're driving at. Thousands of studies have uncovered some mechanisms at the very core of human society. The mechanisms behave similarly enough to warrant a name (kinetic energy, potential energy etc.), and that concept seems to be at the heart of what drives most of society. Not only that, it induces a quantifiable (if sometimes only roughly, or even in theory) property. That mechanism, along with its quantifiable trait is called power. It was found to be roughly "the ability to bend others to your will", and has produced interesting, useful models (qualitative -- not quantitative). You want to give it another name? Fine, call it X. But 100 years ago we did not know about X as much as we do now. If you want to identify X with something that you think has been known for a long time -- you'll be wrong; if you want to identify X with something you think is still a complete mystery -- you'll be wrong again. You want to argue with scientists about the names they choose and then quote someone who says arguing about names is futile -- great. What is it that you're saying?

The concept of power conveys a lot of knowledge that has been gathered over decades. Your responses seem to be like those of someone who's just heard of energy, and says, "If energy is what moving things possess, why not just call it speed? Oh, a ball at the top of the hill also has energy, why not just call it height? Oh, fire has energy too? So energy is everywhere, and if it's everywhere then it doesn't mean anything!" Either that someone decides to learn basic physics, or decides to stay ignorant. But if he decides to stay ignorant, I think you would agree it would be foolish of him to continue arguing.