I think that they can easily put breakable items back into the mix with one simple fix:
Every 25 breakables broken, without killing a mob, gives you a debuff in which you gain nothing from continuing to loot only those AND chests/graves/racks. The debuff lasts for 15-20 minutes, or until you take down a champion pack.
So, if you can break 24 urns and kill some monsters, you don't receive the debuff. This will help curb botters for a little while. People who want to exploit the game always will. There will never be a hard fix for this, unless it hurts the actual playing player population.
Most of the people who were jar farming were doing it by logging out of the game and not killing a single thing.
A debuff would be worn off as soon as the player logs out of the game.
I've also addressed this here.
Instead of just flat out nerfing destructible objects, why not have an internal timer that's applied whenever you kill an enemy. Let this timer last for say 2 - 5 minutes. Much like how Nephalem Valor expires, this will allow players to not be punished for destructible objects.
When this timer is applied, destructible objects will act like they did before the nerf. When the player is not actively killing monsters, destructible objects will be worthless. This way you're still encouraging the player to actually play the game.