Starting at the beginning:
Power = speed x force
So, if you want more power, then you either make more "force" or you make the same force at a greater "speed"
(for rotating machinery, power [kW] = ((Torque [Nm] x angular velocity [rpm] )/ 9554)
so 1Nm torque is 0.1kW at 1000rpm, but 1kW at 10,000 rpm
For an electrical machine (motor/generator) the "torque" produced (or absorbed) is proportional to the volume (and hence mass) of "active" material in the machine (copper & iron etc). hence the overall mass and size of the machine depends upon the torque you want to make.
So, to provide more power, it make sense to increase the rotational speed of the device rather than the torque required/produced. (ultimately, speed is then limited by device cooling and mechanical limits due to centrifugal acceleration etc)
Further to this, for electrical power, the torque is proportional to Current[Amperes], and the speed to voltage[Volts]. As losses (and transmission/conversion costs) increase with the square of current (IsquaredR losses) it makes sense to move power around at the highest voltage possible to minimise the current requires (also why for example the National grid uses 400kV !!)
For a conventional rotating field multi phase alternator, the ouput frequecy is fixed by the rotation speed and the number of electrical phases per mechanical revolution.
To avoid the cost / complexity and bulk of performing an intermediate frequency or voltage conversion, it is best to design the generating system to operate at as stable a speed as possible, and to be able to transmit the resulting AC power directly to the power transmission system.
The result of all this, high power = high electrical AC frequency !