HUD has actually eliminated the old "take one, take all" Section 8 policy as well as the "endless lease" policy, since, I believe 1994. The change has made landlords more willing to accept vouchers, but, as the problems with the "Moving to Opportunity" program show, it is difficult to convince receipents, even with counseling and even with landlord consent, that they should move away from high-poverty neighborhoods. Maybe that is because they understand what the empirical evidence now shows: the benefits are minimal at best.
Update: Congress repealed the "take one, take all" provision in 1998. Some states, however, maintain the provision; there is currently an argument over whether federal law preempts the right of states to have such a provision. Courts in New York and New Jersey have order landlords to keep Section 8 tenants after their leases have expired (see Rosario v Diagonal Realty, LLC for NY, and Franklin Tower One v. N.M for NJ).
I will try to find out more, but so far as I can tell, Tennessee (the subject of The Atlantic piece) respects the repeal provisions.