The Spartans were not illiterate - they preferred oral history and verbal contracts to written records. Similarly they were perfectly capable of building things, yet they preferred that Sparta itself was a city of small buildings without walls. There's nothing left of it today.

Spartans, basically, eschewed possessions, apart from their personal weapons. They didn't want to grow soft and weak, so they made luxury impossible. An adult male Spartan owned some land, which was farmed by Perioikoi or Helots, and he was responsible for providing his share of food to the barracks in which he lived, but he could not "profit", ever. Perioikoi (permanent residents of Sparta but not Spartiate themselves) could and did get rich. Even Helots (slaves from conquered enemies) usually lived materially richer lives than Spartans.

What they should have done was announced that glorious deaths didn't count until a Spartan had had so many kids, that would have made everyone happy.