I don't think this is a good example of what you're trying to argue. It could easily be said that if water was privately provided, rates could be set such that the economics are feasible (everyone needs water - the demand curve is highly inelastic). Competition could ensure the water is pure and fairly priced. Who would go with Company A's lead-laden water if B's is clean?
I happen to disagree with the argument I just provided, but for reasons different than the quality of service a free market would provide.
> Who would go with Company A's lead-laden water if B's is clean?
That's not a realistic scenario however as that implies that each company would set up its own plumbing infrastructure, water sources, etc. In reality, the infrastructure is shared. So I see no reason why the choice wouldn't target be between "company A who has lead-laden water, company B who does some extra purification and charges for it heavily and company C who serves the exact same water as A but has better advertisements."
What would be the incentive to actually fix the infrastructure if it benefited your competition just as much as you?
I happen to disagree with the argument I just provided, but for reasons different than the quality of service a free market would provide.