You can eliminate Ich from an aquarium, BUT, it takes much work and patience. In a FOWLR you can follow hyposalinity protocols for the DT followed by QTing all new arrivals. In a reef tank, the fish need to be moved to a QT/hospital tank and kept there for (ugh!) 6 weeks while you leave the DT fallow for 6 weeks. No host fish...parasites die.
There have been many debates on this site, and others, about adjunct therapies that may help remove ICH from fish temporaly in an acute infection.
While I read these debates with great interest I do not wish to start another one.
Stress...overpopulation, poor water quality, poor water movement, over or under feeding and aggressive fish...all can lead to an outbreak of visible Ich
in an aquarium that has Ich present. But..there are some aquariums that are free of ICH if proper treatment and prevention practices are followed