What advantages to permeability tuning as against capacitive tuning?
The permeability tuning (variable inductance) is essentially a slug of ferrite that can be screwed in and out of a coil wound around a former. Once the circuit is tuned wax can be used to seal it into position or the screw thread can be locked mechanically. The variable capacitor has large inter-meshing plates that are subject to mechanical damage or vibration and is physically a large component (size matters). The range of tuning using variable capacitors is greater than inductive tuning for a single tuning coil. Switching coils (bands) is easy to do.  Variable capacitors are quite expensive (not a military consideration) to produce so there is a cost saving as well. For a portable radio used in warfare size, mechanical robustness and functionality are important.