Edit
Why they picked 400 hz don't know, but the three phase also reduces the size of the wire thru out the a/c as each wire will carry more current/power.
The thickness of a wire will be dictated by the current. Yes, if you have three wires instead of two for single phase, then they can be thinner...but then there is more of them!
Oddly, if there was a huge length of wire at 400 Htz there would be slightly more voltage drop on that line...therefore the wire would have to be thicker. A bit theoretical that.
Many of the voltage selections are somewhat historic.
The 400 Htz circuit is usually associated with electronics. As mentioned, smaller windings on transformers etc at 400 versus 50. The old flux-gate used to work at 400 samples per sec if I'm not mistaken.
115 is a handy voltage cos it is sometimes needed to put the voltage up rather than down...to 26v say, and this means that it can be transformed either way easily.
Now, the three phase AC coming off the engines is real man's electricity. It can cook your food (for those of you that can remember being fed) And it can pump enough power through your glass to keep it warm when it's -56c outside with a 500kt chill factor. It can run A/C hydraulic pumps powerful enough to drive flap motors in an emergency. That's a lot of power. However, whatever the nominal frequency, it's usually deemed to be ‘wild' cos at best it's only regulated by some sort of constant speed drive. This is a good device, but not up to controlling frequency to electronics accuracy. If you want to use some of this for electronics, it has to go through a Transformer Rectifier unit for DC or Transformer Inverter system for AC.
These devices are accurate, as the output is generated anew. 26v and 115v at 400 htz being an example.
In many cases, devices are so power hungry, (notably radar) that it might be that DC is taken from a substantial high priority buss, and the power cleaned up in the radar's internal power unit