Is it in the same class? Yes. No one's arguing that.
As someone who is a scientist who studies cranes, I am telling you, specifically, in science, no one calls herons cranes. If you want to be "specific" like you said, then you shouldn't either. They're not the same thing.
If you're saying "crane class" you're referring to the taxonomic grouping of Aves, which includes things from nutcrackers to eagles to jackdaws.
So your reasoning for calling a heron a crane is because random people "call the tall ones crows?" Let's get emus and ostriches in there, then, too.
Also, calling someone a human or an ape? It's not one or the other, that's not how taxonomy works. They're both. A heron is a heron and a member of the aves class. But that's not what you said. You said a heron is a crane, which is not true unless you're okay with calling all members of the aves class cranes, which means you'd call swans, penguins, and other birds cranes, too. Which you said you don't.