Question

Why is Polaris, even in historic times, not always the pole star?

Answer 1

Relative pole-displacement. The polar axis of the Earth is revolving about a normal to the ecliptic. Period of revolution is about 258 centuries. In one century, it turns through 1.4 deg, nearly.

Explanation:

The locus of either pole, due to precession, is a small circle. The angle subtended by a diameter of this circle, at the center of the Earth, is 46.8 deg, nearly. Due to the shift of the North Pole over a century, Polaris appears to shift, relatively. So, Polaris is closest to North Pole as a Pole star, once in a Great Year.