Who was the director of High Noon?
Well, you're looking at it backwards. The concept of "noon" is man-made. Noon describes that point during the day when the sun is directly (or nearly) overhead. So, to answer your question, the sun is high in the sky at noon because we define "noon" as that time during the day when the sun is high in the sky.
(Viewed from a fixed position on earth) Starting from high noon say, 360 degrees of revolution (sidereal day) takes 23 hours 56 minutes 4 seconds, but in the meanwhile the earth has travelled around its orbit around the sun, and needs to rotate a little further to bring it back to high noon, this brings the high noon to high noon time to exactly 24 hours.