My understanding is that a) who even knows in real life what a "morning star" is, b) from 1e/UA, a morning star is a large blunt instrument with significant (as in, 3-inch-long or so) spikes and no chain – I think I remember one description saying it was entirely of wood, but with the metal spikes, and c) this carries into 3e, by virtue of morning stars being classed as simple weapons, and chains make a weapon complicated.