Why to use 50/60 Hz Frequency and Not other Higher/Lower Values?
Wikipedia explains it fairly well in their article Utility Frequency:

The induction motor was found to work well on frequencies around 50 to 60 Hz, but with the materials available in the 1890s would not work well at a frequency of, say, 133 Hz. There is a fixed relationship between the number of magnetic poles in the induction motor field, the frequency of the alternating current, and the rotation speed; so, a given standard speed limits the choice of frequency (and the reverse). Once AC electric motors became common, it was important to standardize frequency for compatibility with the customer's equipment.

Generators operated by slow-speed reciprocating engines will produce lower frequencies, for a given number of poles, than those operated by, for example, a high-speed steam turbine. For very slow prime mover speeds, it would be costly to build a generator with enough poles to provide a high AC frequency. As well, synchronizing two generators to the same speed was found to be easier at lower speeds.

Generally, lower frequencies require more iron. You may like to think of this as a magnetic store of energy per cycle: the shorter each cycle the less iron is needed. Since weight is a bigger consideration in aircraft design than cost is they standardised on 400 Hz AC systems.

Lower frequencies are better for long distance power transmission as power losses are reduced. DC, with a frequency of zero, is best although step up to and down from high voltage is complex.

All engineering is about finding the "least worst" answer to the problem 50 / 60 Hz is a good trade-off between the factors above.