Although thermodynamically feasible in practice alumina is not reduced using magnesium. Why?

Temperature above the point of intersection of Al₂O₃ and MgO curves, Mg can reduce Al₂O₃.
But the temperature required (1600 K) is very high.
Hence the reduction process will be uneconomic and difficult.
${\mathrm{Fe}}_2{\mathrm{O}}_3 + 2\mathrm{Al} \stackrel{1000-1500°\mathrm{C}}{\to } {\mathrm{Al}}_2{\mathrm{O}}_3+2\mathrm{Fe}$
The ignition helps to overcome the energy of activitation and hence the reaction is fast.