The underlying reason is that Line accepts x,y coordinates, while GeoPath accepts latitude longitude pairs (which is kinda y,x).
Can indeed be solved in many ways:
coords = EntityValue[GeoEntities[Entity["Country", "Australia"], "City"], "Coordinates"];
route = Last[FindShortestTour[coords]];
GeoGraphics[{Thick, Red, Line[Reverse /@ coords[[route]]]}]
GeoGraphics[{Thick, Red, Line[coords[[route, {2, 1}]]]}]
GeoGraphics[{Thick, Red, GeoPath[coords[[route]]]}]