Why do they do this? A typical truck engine might produce 200-400kW and even an extremely large LED array and sound system would only consume a few kW at most. Wouldn't it be simpler and more efficient to upgrade the original vehicle's alternator to supply the required power rather than adding a whole additional 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.
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.