....Sumerian Phalanx?

 

What did it in to the Sumerian phalanx, was the emphasis on numbers of archers with composite bows by the Akkadians.  The "chariot" did not make an appearance in Mesopotamia until about 1800 BC, (i.e. after the time of the Sumerians).   Prior to this, the Sumerians were using the "battle wagon", moved by either onagers or donkeys.  They were not very effective on the battlefield being slow and not having the ability to make turns, but were mainly used to simply charge into the enemy while the occupant threw spears at them.  At this time the only thing that they could do was to increase in speed or slow down (and make wide turns). 

Not sure you'de call the Sumerian formation a phalanx. It was more a line of spears, I think phalanx implies a deep formation.

 

We have the examples of the Standard of Ur and the Stele of the Vultures which show a formation of 10 to 11 men per row and 6 rows deep.  Since their spears were relatively short they could turn in either direction making their formations 6 per row and 11 men deep.  Another interesting thing to note is that they held their spears with both hands with the shield slung on one of their arms......just like the Macedonians.

 

Sure but they could still flank a phalanx very easily. Flanking was doom for phalanxes.

 

Again, they were not very manueverable and relatively slow.  They were used for crashing into the enemy's formation, not for flank attacks.  Even if they could be used in such a way, the Sumerian phalanx was flexible enough in whole or in part to face that attack.  By the way, the earliest descriptions of battles involving true war chariots seem to be describing massed attacks, not flank attacks.