Why not run high power truck-mounted electronics from the truck's engine?
A typical truck engine might produce 200-400kW [...]


That is mechanical power. Electrical power is generated in the alternator, and thouse typically generate power in the order of 1 kW, as that is enough to power the lights and charge the battery etc.

The dedicated power generators are also more fuel-efficient, and can produce higher voltages - a big truck operates at only 24 Volts. Light and sound installations in the multi-kW range will usually need 110 or 230 Volts to operate.

EDIT:


  Wouldn't it be simpler and more efficient to upgrade the original vehicle's alternator 


It would be simpler only when there is space available for a bigger alternator and when there is a bigger one actually available.

But it would never be more efficent in fuel: The generators engine is highly optimized for its task (hopefully), and will be operated at or near its point of maximum efficiency. It will also be a lot smaller, as you need only a few kW instead of 100 or more. This has a big effect in fuel consumption.