you have no idea how much mail can pile up at the routes if you deliver 3x a week.....and you cant mandate a private company to do anything.....if you did be prepared for them to charge exorbitant rates to do it....Except the Private Sector won't do the job.
They'll do what they can make money doing. If there's no money to be made sending stuff to Aunt Gertie in the sticks, they won't do that.
They can just mandate the private company deliver to the rural areas. Also there is no reason a 3 day a week delivery schedule would not serve the rural area well enough.