Jack Painter wrote:
"I may have missed any theory about the 1/4 wavelength being the optimal
height---."

I missed that too, unless your aim is near vertical incidence reflection
from the ionosphere for nearby contacts. Some hams have that goal and
argue that 1/4-wave height is enough because it gives the first
elevation that produces the drivepoint impedance of the horizontal
dipole in free-space.

The purpose of the antenna is communication, not impedance. A friendly
impedance helps of course.

Best regards, Richard Harrison, KB5WZI