Relationship between latency and sampling rate of a digital PID controller
The sampling rate needs to be more than twice the maximum bandwidth of the signal you wish to process. This is to avoid a phenomena called Aliasing.

In the above diagram you can see the problem; a single set of samples (dots) taken from the red waveform can be mistaken for the blue waveform.

the sampling rate should not be chosen to be much larger than the
closed loop bandwidth because that's overkill.

Because you need to use an anti-alias filter between your real world signal and the ADC, you should try and sample a lot higher than twice the signal bandwidth so that the filter doesn't attenuate any in-band wanted signals and the filter has enough spectral area to attenuate higher-than-wanted frequencies to a reasonable low level.