It is easy to maintain and change the voltage of AC electricity for transmission and distribution. Plant cost for AC transmission (circuit breakers, transformers etc.) is much lower than the equivalent DC transmission. From power stations, AC is produced so it is better to use AC than DC instead of converting it.
Then, what is the main advantage of AC over DC?
The major advantage that AC electricity has over DC electricity is that AC voltages can be readily transformed to higher or lower voltage levels, while it is difficult to do that with DC voltages. Since high voltages are more efficient for sending electricity great distances, AC electricity has an advantage over DC.
Why is AC cheaper than DC?
So we generate AC because AC generators are simpler. We transmit high voltage AC across the grid because its more efficient than low voltage. DC generators are more complex. DC has no easy way to change voltage, so DC stations send electricity at the same voltage that it is used at the destination, a low voltage.