Permeably tuned coils take up less space, which is why they might be preferable in a portable radio and especially in a car radio. They were used from time to time in home radios of all makes and models (Airline, Philco, Zenith, etc.). Instead of having a huge tuning condenser, as they were prior to transistor radios with mylar insulated tuning condensers, the radio could contain a small fixed mica condenser and have a tunable coil instead. The coil had to be there anyway, and so making it tunable got rid of the huge condenser. The reason why noone made compact tuning condensers that used mica as the insulation is because mica will wear away if it is sandwiched between the moving plates, which will change the capacitance coverange and eventually destroy the condenser. No plastics were availabe at the time that could perform any better than mica, either. The mylar used in the 1950s and later (and other variations of this type of plastic) can take plates rubbing against it without changing thickness or breaking. Air insulated condensers cannot be made small because first air does not decrease capacitance to the required value as much as plastic or mica, so there must be more space between the plates. Second, if the plates are placed very close together with only air as insulation, they may touch and short out. With mylar, the plates can be placed right up against the plastic with no danger of shorting out.
Thomas