Why is the Digital 0 not 0V in computer systems?
You are getting confused. Look at TTL for example: -



A low input level is between 0 volts and some small value above 0 volts (0.8 volts for the case of TTL).


  why do we take the trouble to set the 'low' to any positive voltage at
  all?


We take the trouble to ensure it is below a certain small value.

Picture from here.