I'm sure the new Empire banned Tiber Septim and outlawed the Blades because of their connection to the Septims. They don't want people to worship the Septims because they want to be recognised as the new rulers and not constantly be under the shadow of a previous dynasty.
Still, banning a cult around a dragon god is not necessarily the best course of action. It'd be like if all the European countries had banned the Catholic Church after they went from "emperor by god's grace" to "democratically elected parliament".