I've found an interesting reading that shows how essential DOC can be for fish survival under specific conditions.High DOC, similar to high nitrate, is an indicator of general pollution, as some compounds are toxic to fish at high concentration. I also read that high DOC can trigger algae, so heavily stocked tanks can become an algae farm unless DOC are removed by Purigen as recommended. Barr has done an experiment to add more and more minors to a planted tank and eventually algae popped up.
For example, Amazonian Rio ***** is a very acidic environment, and blackwater DOC protects fish from going belly up in this harsh environment.
This source also points out that DOCs are not created equal as you mentioned. There are also lots of papers that discuss how DOC reduces toxicity of Copper, Aluminum, Zinc etc for fish (and shrimps)...
I can also see that DOC can be toxic. Say if I dumped a bottle of vinegar into the tank, I am sure fish would not be that happy.