With many kinds of AC motormotors, the rate of rotation will be strongly correlated with the frequency of the driving current. In many cases, the rotational speed in revolutions per second will either be an exact fraction of the drive frequency in cycles per second (e.g. 1/3), or else an exact fraction minus a certain amount of "slip" which depends upon the drive voltage. While it may be possible to control the speed of some AC motors by varying the drive voltage and thus allowing varying amounts of slippage, it's more efficient to vary the drive frequency and try to minimize slippage.
Note also that nearly all motors that are capable of doing a non-trivial amount of work require that the polarity of current in some of the coils be periodically switched. This is just as true of DC motors as AC ones. Most DC motors use a mechanical commutator and brushes to perform such switching; these tend to have a limited useful lifetime before requiring service or replacement. Some use electronics to switch the actual motor current, but that essentially turns them into an "inverter-plus-AC-motor" combination.