Imchlo 

Is the use of chlorine environmentally sustainable?

This largely depends on how it is dosed, used and monitored.
In general it can be stated that the current method of dosage and monitoring in industrial cooling systems is not the most sustainable method because, in almost all cases, an excess of hypochlorous acid is dosed.

Because of this over dosage, side reactions occur that produce unwanted AOXs (absorbable halogenated hydrocarbons). These can be released into the environment.

However, if overdosage can be avoided by eliminating the unwanted side reactions, and  using the active material, hypochlorite, primarily for killing bacteria, the formation of these AOXs would be greatly reduced and even disappear completely. This would give chlorine a major "sustainability boost"

That is exactly what DMH does!