If the majority of the landowners in any wet, swamp or overflowed lands petition the court for a drainage district based on the widening, deepening, cleaning or straightening of such natural streams only as the United States government or the state drainage authorities pronounce as essential for the drainage of such lands, and agree in the petition to a tax levy for such draining, spread equally over each acre, then the court shall entertain such petition and all proceedings shall be in accordance with the provisions of this chapter, except that the viewers shall not classify the lands as to the benefit derived. Furthermore, in any case where it is made to appear, after the natural stream has been widened, reopened, cleaned out or straightened, that the majority of the landowners of any district, formed under the provisions of this section, desire that such district be divided into subdistricts, the court may, in its discretion so order.