Others have answered this pretty well, but a bit more:
The higher the frequency, the less inductance is needed in magnetic
components. Fewer turns of copper and less iron core (alternators,
motors, transformers etc) which means less weight. This was and still is
a critical factor in aviation and every Kg saved is more freight or less
fuel. If you look at the avionics fit for some a/c in the 50's and 60's,
it's surprising that they ever got off the ground, but they just put big
engines in :-).
Higher frequencies have been used in the past, even as early as ww2,
with some post war uk mil aircraft, ie Lightning and Vulcan using 1600
Hz supplies in places. At this frequency, you need fairly exotic and
expensive magnetic materials to keep losses down. Acceptable in the cold
war, but too expensive for commercial use and by that time, 400Hz
supplies in a/c had been around since ww2 at least and there was a whole
infrastructure in terms of components and standardisation.
As an example, a 1kva 50Hz transformer would be quite heavy and take
two hands to lift, while the 400Hz equivalent would fit in the palm of one
hand...
Regards,
Chris