Greek half-kneeling archers

[Alanus]

The method using the ground as a fixed point to lever against would result in the leg being free after stringing, allowing an immediate shot from a crouching position. That this would be advantageous in battle is moot, but a culture that invents a foot-race carrying a heavy bronze-faced shield could easily evolve archery competitions requiring this sort of "showy-move".

Do you have a priori written examples of this "showy-move"?  I have never heard of an instance where an archer went into the fray with an unstrung bow, then stringing it at the battle-front. Any foot-archer in his right mind would string his bow just before falling into formation. If he was a "barbarian" (add your own ethnos--- Scythian, Sarmatian, Turk), his bow was already strung and cased before he swung into the saddle. Romance and showmanship might be fine for Hollywood, but not in the realism of actual battle.

You would be correct with the bow-end on the ground premise if the archer was a really ancient Egyptian or Middle Ages soldier. In both cases, these archers used "self bows" or "long bows" made from a single shaft of wood. Such a bow could be built with 2 day's labor. We have illustrations of your method, although from a standing position; and (again) its rather doubtful the bow was strung on the battlefront. (Such a method was also favored by 19th century women.) In contrast, the Greeks used composite bows. The design actually goes back to around 2,000 BCE with the initial introduction of bent-wood technology, made from sinew, a middle wood spline, and horn, a laminate fused with slow-drying fish glue. Such a bow required at least a month to create. They were not tools but prized weapons.