Hi Roland,
I am certainly not and expert and have never seen such sword outside this forum, but I do have some ideas. Persian shamshirs are chiefly a cavalry weapon, and I think this is the main reason they look like this. The velocity of leading to impact comes mainly from the movement of the horse, not of the arm and is therefore much too powerful for a normal, man to man sword. In fact, I think it is usable, but not very effective as a duel weapon.
A mild curve can be effective both on foot as on horseback, but such extreme curves are meant for cutting from horseback in gallop. A blow from a straight sword in gallop would not make a cutting motion which needs to be diagonal (knows everybody who cuts his bread in the morning, try to imagine hitting your stake with a knife). A high speed blow simply has no time to make the diagonal movement and that has to come from the shape of the blade. If not, it would not be very effective and can knock the sword out of the swordsman hand. The subject of cutting is relatively far and hit by the middle of the sword, as you said, and then, the sword recedes sharply to make the diagonal for cutting.
This type of cutting also explains why shamshir as well as akilij have hooked pommel: to prevent the sword being knocked out of the rider's hand upon high velocity impact.
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