Find settling time of ADC
The problem is that each bit, from most significant to least significant, must have the same analog resolution, so the input settling time requirement is unchanged regardless of how many bits are being acquired.

As an example, let's say you are using a 12-bit ADC with a 10-volt input. 1 lsb is 10v/4095, or 2.422 mV, and the transition of the msb occurs at a nominal 5.00122 volts. The transition of the MSB at a count of 1FFH to 200H must be located to the same resolution as the lsb. If it is not, the entire accuracy of the 12 bit word will suffer.

So acquiring a signal by 1-bit ADC (and such things do exist and are extremely useful - look up "sigma-delta adc") with 12-bit precision requires exactly the same input accuracy as acquiring all 12 bits. It's quicker, but needs to be just as precise.