According to two military Kiltmakers that I have talked to the elastic is there to prevent inadvertent blowing up of the Kilt while on parade.

Because members of a military band on parade cannot reach down to hold their pleats in the wind without breaking formation they started putting the elastic there to serve that function without totally destroying the swish.

You can leave it in or remove the elastic if you wish. It serves no purpose on a civilian Kilt.