Degrees of latitude can only be equidistant on a perfect sphere with parallel light rays from an extremely distant North star.

Degrees of latitude have no meaning whatsoever on a flat plane. All you've measured is the angle to polaris. Where would you draw the angle of latitude?

Also, you've skipped completely over people in the South, and how to determine longitude.

EDIT: Let us presume for purposes of this thread that we have an observer on a globe/sphere Earth looking at Polaris;

All vertical lines P lead to Polaris. The observer has a horizontal H, and measures 30 degrees above his horizontal as the elevation to Polaris. Simple geometry shows that if his angle E = 30, then the angle between the two radials to the equator and to his position, angle L, also = 30.

Simple geometry tells us that for a sphere, the length of an arc on the surface is consistently the same, whereever the 30 degrees is measured; 30 degrees down from the pole, 30 degrees up from the equator, the arc will be the same length. Equal division of the circumference into equal parts of one degree, etc.

Thus the distance between points can be calculated and used as a basis for navigation, and thus the nautical mile, a length of arc based on subdivision of a degree of latitude or longitude into equal parts, was born.

Observing angle E tells you what angle L is.

All that would appear to happen with the FE angle to polaris diagram above is that you determine the angle to Polaris. Where is the angle of latitude to be drawn?