Why do jet generators produce a higher frequency power then household electricity?
This is a bit speculative, and if I am wrong, I will stand corrected. 

Based on my little experience with power plant gas turbines, the frequency depends on the rpm of the turbine and the number of poles of the generator. A power plant turbine runs at 3000 rpm (for 50 Hz) or 3600 rpm (for 60 Hz), with two poles (this is the most reliable design, and works with turbines with rotors up to about 4 m diameter. 

An aircraft APU is much smaller, and will run at higher for optimized power output. So, for the 400 Hz, you would have, for example, 12000 rpm and 4 poles (or 24000 rpm and 2 poles).

It already has been mentioned that transformers can be way smaller and lighter for higher frequencies, and it may also be that the higher freqencies of the harmonics cause less interference with other systems of the aircraft.



The speed of the generator is held constant, regardless of the engine's rpm, by the use of a Constant Speed Generator or Integrated Drive Generator.