From Wikipedia: "A nutrient is a component in foods that an organism uses to survive and grow. "
I'd say the primary for survival is energy. Sugars (carbs) are very high on that. There are of course secondary nutrients like eg amino acids in protein that are very important.
My opinion ultimately doesn't matter on this. I was just speaking to the saying.
That said, it is trivial to find primary items for survival if we just discuss things you would die without. Consider, water has zero calories, but you would die without it.
But your interpretation of nutrients do color your interpretation of "empty calories". Unless proven otherwise, I'll stand by that it's a useless phrase distracting from the conversation of nutrition.
It is a shortening of "empty [of nutrient providing] calories." This is pretty straight forward. If you were to eat nothing but sugar every day, you would die. Same as if you drank water, which is "empty of caloric or nutritional" content.
Are they worthless? No. They do provide caloric value. But they do not provide any nutritional value. This isn't even really at debate, is it?