Frequency coming from your wall outlet is 60 Hz and is held very steady.
Remember that the generating station is using HUGE generators, HUGE! the rotating rotors weigh many tons and through the grid are locked into generators from other power plants, slowing down a generator would cause havoc on the grid and the other generators would try and pull it back into sync.
Ever see a generator being brought up to speed? It must be precisely matched to the speed of other generators on the grid and MUST be exactly in phase or a disaster could easily happen. Could wipe out the generator and part of the grid.
Every cycle is counted and usually around midnight the generators are slowed or sped up if a few Hz needed to be added or subtracted.
Remember the old clocks on the wall? They never lost time, they relied on a steady 60Hz feeding the motor and simple gearing to work.
Early TT used that steady 60Hz to maintain a precise speed like the clock. Of course slippage from the driving elements can not be accounted for but the motor always ran at a proper speed.
BillWojo