Why does disk loading mean anything when rotors/propellers are not disks?
The disc model is used wherever generalities of behaviour are studied without the need to know individual blade characteristics. It captures the mathematics of those generalities in a simple way that leaves out extraneous detail which would make the maths impossibly laborious.

Typically the aircraft designer will use the disc model in the design of their airframe, leaving the blade details for the propeller or rotor designer to figure out.