NPN is physically symmetrical yet the model isn't?
The design of the schematic symbol does not represent the actual geometry of the semiconductors' (n- and p- types) being used. Rather, it is derived from the original bipolar junction constructed by John Bardeen and Walter Brattain.

You should also note that in a bipolar junction transistor, the outer n-type semiconductor in a NPN (or p-type semiconductor in a PNP) may not necessarily have the equal concentrations. They could also have a completely different construction than the one shown in your screenshot. But the primary construction is, indeed, two semi-conducting materials of the same type (but not necessarily of the same charge concetration) being physically separated by a layer of semiconducting material with charge concentration opposite that of the outer semiconducting materials.