Why is MnO4- not a complex ion yet it has color?
Complex ions are not the only ions that have color in solution. For example, Cu2+ is blue in aqueous solutions but is not a complex ion.
That's correct, but you haven't answer the question. Mn and Cu are transition metals that have d-orbitals available. One of the properties of the d-orbitals is that they can unfold and allow electrons to move freely in those unfolded orbitals. The energy the electrons lose is in the visible range of the spectrum, so we see it as colour.