The state or any of its subdivisions shall have authority to provide for the elimination of intersections at grade of controlled access facilities with existing state or county roads, and city or town streets by grade separation of service road or by closing off such roads and streets at the right-of-way boundary line of such controlled access facility. After the establishment of any controlled access facility, no highway or street which is not a part of said facility shall intersect the same at grade. No city or town street, county or state highway or other public way shall be opened into or connected with any such controlled access facility without the consent and previous approval of the Director of Transportation; provided, that the Director of Transportation may, whenever he determines that traffic is not thereby impaired, authorize the continued intersection at grade of lightly traveled entrances and minor public roads as ways of access to controlled access facilities in sparsely populated areas.