Why does K⁺ have 0 valence electrons?
What you say is correct.  The  [Ar] configuration we are left with does have 8 valence electrons.  But I think it is just semantics.  Elemental potassium has an [Ar] 4s1 electron configuration.  One would say it has one valence electron.  If we take that one valence electron away, it makes sense to say that it now has zero valence electrons because "1 - 1 = 0".