I don't consider gar trash fish. Gar do not ruin watersheds. Gar are not an invasive species to our waters. If gar are the only fish present, it isn't because gar preyed upon the other fish. It's because the water quaility is poor, and the gar can tolerate that more than most species.
Carp, of all species are trash fish. White perch are a trash fish.
At the same time, that doesn't mean all "invasive" species are not sport fish.
Trout, are not native to this state, and therefore, are an invasive species.