The state highway commission, alone, or in agreement with any county, city, town or village may designate and establish controlled-access highways as new and additional facilities or may designate and establish existing streets or highways as included within a controlled-access facility. The state or any of its subdivisions shall have authority to provide for the elimination of intersections at grade or controlled-access facilities with existing state and county roads and city or town or village streets, by grade separation or service road, or by closing off such roads and streets at the right-of-way boundary line of such controlled-access facility; and after the establishment of any controlled- access facility, no highway or street which is not part of said facility shall intersect the same at grade. No city, town or village 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 state highway commission. Such consent and approval shall be given only if the public interest shall be served thereby.