Hm. I don't think there is anything wrong with having terms defining paraphyletic groups. I don't think we need to treat fish or plants for that matter as a monophyletic group necessarily in order to avoid misinformation. The group that includes algae and plants is monophyletic after all, but I don't know what that has to do with the original point.

"Are algae plants?" "Yes."

Is incorrect. That it once stood as the best available information is interesting but not relevant to the veracity.