First the Spartans trained full time for war because they used serfs to grow their food and make their equipment. They were called helots. As a rite of passage, Spartan boys were let loose in the countryside as a lesson in survival and they reportedly also killed stray slaves as practice and as a means of keeping the helots in line. It was a different time and a different people.
As to killing the wounded. I seem to recall that the Spartan spear had a spiked butt and that while ther rear ranks had their shoulders into and pushing the ranks to their front, they used that spike in a piston fashion on the enemy they were trudging over.
No quarrel with your customary grasp of history..... but among Leonidas' great strengths lay other traits which would be fatal today. What started me on this after the movie was the thought that we seemingly have no such figure today - then I began to question whether such an individual in this world could replicate his immortal stand...... or would he be a modern day Custer?