my thoughts ,.. the rotors was already faced once , the chances of there being much left to face off are slim . but if there is enough left to face off you still have relatively thin rotors compared to when new ... thin rotors are always a problem , but its not a wear problem like most assume , it is purely a heat problem .
the biggest cause for complaints with brake pulsations with turned components is very rarely from the rather poor job of machining most of them get .
after all calipers float and will absorb a lot more run out then most expect .
nearly always the cause is from the rotor being heated up during brake pad break in .. or if the person who did the brakes did not break in and seat the brakes properly
they warp from overheating during normal use .
it takes a lot of heat to properly seat in brakes .. or if not seated properly they create more heat in normal use ... heat is the death of turned rotors .
Brake pulsation is never due to run out, it is always due to thickness variation. Excessive run out is also bad, but in a different way; it causes low pedal on initial application. Yes the caliper design will allow for some run out whether it is a floating mount set up or opposing pistons. But with excess run out when the brakes are released the wobble in the rotor pushes the pads apart further so there is space between them and the rotor. When the brakes are next applied, that additional clearance must be taken up first before any pad pressure can happen. In normal use it is the minute deflection of the square cut o-ring that draws the piston back so very slightly to release the pressure of the pad against the rotor. The pads will always drag very lightly on the rotor in normal conditions. It takes very little additional clearance to cause low pedal due to the large size of the caliper piston compared to the small diameter of the master cylinder.
Thickness variation causes pulsing because there are essentially thick parts of the rotor where the pads grab, then a thin spot where the pressure is reduced. If you apply the brakes hard enough, the friction may remain relatively constant as far as the braking action, but then you will feel the pulsing in the pedal as the pads are forced in and out on the rotor thus causing the caliper piston to oscillate and then transferring that action through to the master cylinder and the pedal.
Modern rotors seldom have much extra material for machining once let alone twice as you noted. Too often even a properly machined rotor that is still within the minimum thickness will still warp as the reduced mass decreases it's heat absorption capacity. Of further note on the minimum thickness, it is the
minimum wear thickness, not the minimum machining thickness. There must still be sufficient material after machining to allow for wear in use so that the minimum thickness is not reached. This is a common error made by many, if you machine it to the minimum, it is now worn out without ever having been reused. Typically at least an additional .030" - .040" of thickness should be left for wear.
As for seating in of pads, that is less important in average cars with common brake materials. Some exotic pad and rotor materials used in performance application and or racing do need to be seated in properly. This process causes a transfer of friction material from the pad and embeds it to the rotor surface creating far greater friction properties.