Water would have to be pretty contaminated to require distillation wouldn't it ? As opposed to just boiling ?
That depends on the chemical(s) in the water.
Boiling only kills and neutralizes the stuff that will evaporate or become neutral from the temperatures. We have a lot of heavy metal contamination which will stay right in the pot or concentrate from boiling.
Distilling fixes all the heavier than water mass objects, the living nastiness and some of the chemicals. It does not do much for the ene's or hol's type stuff. A lot of that goes up the pipe in evaporated form unchanged by the temperatures and collects and reforms on the other end of the coil. Again re-concentrating in the capture vessel.
If you want to get rid of VOC's (volatile organic compounds) then carbon filtration and distillation is required. Even then there are probably a few VOC's that require more steps or a repeat process to get pure H2O.
Open air ground water in Ohio is pretty bad in some places. Benzene and toluene like chemicals make distilling just one part of the process.