As I wrote in another thread, it's probably due to the universal appearance of it in popular history. It's very recognizable and quintessentially Roman, so it's popular amongst illustrators. This has fixed the image of the LS-wearing legionary in the public mind. As a result, many people now assume that all legionairs wore LS (never having seen any other), even though little to no popular history states this is the case.
Little is known about the Roman military preceding the Punic wars, and Romans themselves only became interested in history following the second Punic war. Hence most of Rome's early history has to be guessed from legends and stories. Adrian Goldsworthy speculates that in the early days Romes military consisted of "heroic" combat in Homerian style (essentially stone-and-stick throwing contests with a few armoured guys on chariots getting all the headlines). As the Roman middle-class grew stronger, this transformed into hoplite warfare, until defeats by the Gauls and/or Samnites forced the Romans to adopt the legionary style of warfare. I can't answer the detailed questions, though. I do know that the Camillian legion war preceded by the Servian army, who were IIRC hoplites but already had some sort of hastati-principes-triarii division (the word hastati means spearman, after all).
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