I suspect Plato is what you were thinking of.
Due to battle deaths, male lines tended to die out, and heiresses inherited. When they married already rich guys, wealth became concentrated in fewer families, resulting in fewer Spartan peers to form the phalanx.
In later Sparta, several attempts were made to split up the land between more families so more Spartan peers would be available. But the motivation behind this was profoundly conservative, even reactionary, so I’m not sure even this would be reasonably called “left-wing.”