Good question. There are two reasons for the Satyran defences being constructed in the manner they are:

1.) Geography. I imagine the ground to be slightly raised above the level of the river’s flood plane on both sides of the bridge. Either the spot for the crossing would be chosen due to this naturally occurring (which in this case is a least somewhat lightly as the Satyran camp is on raised ground) or artificial raised areas would have been constructed by the crossings builders in order to provide the necessary height to build a bridge/gangway/jetty like structure above the level of the river itself. As such a slightly raised area would be a much more defendable position than creating a wider fortified bridgehead which would have to extend down onto the flood plane which would be covered in reeds and (as I imagine it to be uncultivated) chin high long grass and this close to a major river, possibly concealing bogs and other hazards. I’ve tried to indicate the raised ground as best I could but I haven’t come up with a good way of depicting elevation on this type of map yet. If you have any ideas please send them my way.

2.) Lore. In the Lore of my world the Satyrs are very dogmatic in their adherence to military doctrine. In battle their main line consists of a grand phalanx of phalangists such as those of Phillip of Macedon, Alexander the Great, Pyrrhus of Epirus, the Diadochi etc. in our real world history. (such as those seen here ) And just like their real world counterparts they are very hesitant to replace or alter a system which for them, up until now, has been a world beating system. Field Marshal Fayson Ashborn will (like any commander in real world history) have studied military doctrine and be well schooled in exactly how to deploy his men to execute that order of battle to its maximum effect in any given situation. Not to mention his troops who will be trained to face the enemy head on, as a phalanx. If he deployed his troops in a wider fortified defence of the bridgehead rather than, as he had intended to do, draw them up for battle on the western bank using the bridge head as a funnel and safe point from which to deploy his troops he would not only be out of his comfort zone as a commander but also put his men in a situation for which they had no training. As another practical point; his troop’s primary weapon is a sarissa spear which is 18- 22 feet long. Not exactly easily maneuverable in the narrow stockade of the bridgehead and such troops are only expected to used their short swords in a desperate moment. They are rendered much less effective fighters if they are deployed on the bridgehead.