My point is that individual States have their own systems headed by a Senator.
No, that's two Senators, and they do not lead any State. States are led by their executive; the Governer. Where did you learn your civics, and what were you doing instead?
Whereas the President is the head of state for the total "immaterial" population, representing a single system.
No, the President is the executive of the collective United States, each State populated by its citizens, who are also represented in each district in each State by an elected Representative of Congress and two Senators in each State. You, individually, are represented in federal government by a President, by a Representative of your your federal district, two Senators of your State. In your State, you are represented by a State Representative and a State Senator of your State district, and a Governor of your State. Get it?
It would therefore be more logical if individual States were regarded as "immaterial" when electing the National head of state.
I did not say that citizens of States are immaterial. I said that a nationwide election of a President is immaterial. Read what I write, not what yuou want to read.
That's what you have. one person of many persons in each State, regardless of the population of each State. Your state is apportioned a number of electors according to your State population. It is not a nationwide vote. It is an election by States.
Why do you regard the people of the U.S.A. as immaterial?
I do not regard the people of the USA as immaterial. Get it? I've laid out your personal representation n government. Is that immaterial?