NavList:

IMHO the poles are interesting all year round.

With P being one of the poles, AP the (assumed) position and GP the geographical position of the sun, when P and AP coincide the navigational triangle is reduced to a line between two points (or better an arc being part of the meridian running through GP) and there no longer is a LHA nor an Azimuth. Whereever you look is to the other pole, so either South or North.

Near the poles, I believe the text is correct, although it will be very hard to either measure or calculate by use of the spherical law of cosines.

I would say this is a quirk in reality, rather than a quirk in the text.