It is important to realise that there is a difference between electrical isolation and radio frequency isolation. Electrical isolation merely means that two conductive materials are separated by some imsulating material. At radio frequencies it is possible for seperate and electrically isolated conductors to pick up radio frequency energy from one another. Several antenna designs such as the Yagi antenna have director and reflector elements that are electrically isolated from one another. All the beam shaping is done with isolated pieces of metal arranged along a boom. Analogue (and digital) TV aerials are a typical example of this type of antenna.
The difficulty of designing efficient antennas for aircraft or satellites is that the antenna either has to have two equal sections working against each other such as a half wave dipole, which is made up of two quarter wavelength wires attached to the inner and outer conductors of a coax cable respectively, or the transmiting element needs to operate against a ground plane.
So while on the ground the earth itself acts as half of the antenna, but as soon as you get up in the air some part of the aircraft needs to become a replacement for the ground in an unbalanced antenna system. The tail of the aircraft can become the radiating element and the wings or body a replacement for the earth. Even in composite bodied aircraft there is enough metalwork to perform this earth function.
Unfortunately the demands of lightning protection mean that all parts of the aircraft need to be electrically bonded together, so it is difficult to find a large isolated panel,or area that can be easily used as a radiating element. The tail fin is generally the best compromise being at the back of the aircraft and away from many sources of electrical noise and interference.
The down side is that conductive dirt layers can build up bridging the electrical isolation of the antenna radiator section due to deicing operations, salt laden atmosphere, rain and general ageing. This reduces the efficiency of the antenna and can allow the introduction of electrical noise from elsewhere in the aircraft. Rain and hail in particular can carry static electrical charges that will absolutely wipe out short wave signals for as long as the rain or hail persists. The only thing that can be heard is a loud crackling noise.
Aircraft should be kept clean and the correct precautions taken when repainting to avoid bridging any electrical isolation areas. Similarly the electrical connections between "earthed" areas of the aircraft need to be kept clean to maintain a low resistance path.
It is a sad truth that most electrical faults end up being traced back to a mechanical origin. The most useful instruments for an electrical engineer are a good pair of eyes and a keen sense of smell (for burnt out components). All the meters and test gear tend to play a secondary role.
It is surprising how often the old, "try unplugging it and plugging it back in again" works too! The reason for this is that a fine insulating oxide layer can form on plugs and sockets. Unplugging and plugging equipment back in scrapes away the oxide layer and completes the electrical path once more.