Pulsations in brake pedal: The discs/rotors seldom pulsate because they physically got "warped".
Most of the times that is felt when using cheap pads (or not correctly bedding the pads after replacement), because the friction material removed from pad will deposit in un-even patches on the disc surface and those will pulsate the brakes. Those "high" patches on disc will heat up, harden, and extract more and more material from the soft pads and that material will be deposited in the same patch making the situation worse.
People blame the rotors when is fact is their choices and know-how.
Related to this:
Same cheap pads will sometimes have hard inclusions in them from factory, and those will score the discs.
Or they are soft enough to trap and embed harder dust particles (especially if driven off road) and score the disc also.
LE: When I said "cheap" I meant cheaply constructed, not cheaply sold. There are pads out there that are cheaply constructed but sold at a premium, because good marketing. Brembo, Akebono comes to mind, they tricked me in buying their products only to have replaced them because various issues (Brembo are hard on discs, won't deposing any coating on them and they are squealing at low speed braking, Akebono don't bite well cold and have a short compression, they don't modulate as well as the OE Advics).