If the sun is about 3,000 miles away (the length of the USA from east coast to west coast), and the radius of the earth being about 10,000 miles, then the sun should be visible all the time from any point on the earth and never set completely, no?

I would understand the sun disappearing (perspective) if the sun was much closer to earth, or of the earth was much larger, but given these proportions, I don’t understand.

Thanks!