The Linux CPU frequency governor literally uses it as part of the algorithm for calculating its sampling rate (i.e., how frequently it checks whether to adjust the processor's frequency).
> Please also read about Intel's "Speed Shift". While it's fairly new (only debuted in 2015), it means the CPU can clock up by itself without waiting for a transition command from the OS.
Hardware-managed P-states don't need to wait for the OS to send a command to change the frequency, but the processor still performs periodic sampling to determine what the frequency should be (this happens ever millisecond on modern AMD and Intel hardware), the processor isn't necessarily going to choose the maximum frequency right away, and it's still subject to delays from the OS (e.g., Windows core parking).
In any case, a multi-millisecond delay in switching frequency isn't because the processor is waiting for the voltage to increase.