The issue is Dices memory management within Mantle. No other Mantle title (Plants Vs Zombies included) has memory issues. Mantle gives more control to the developers, that's what they asked for, that's what they've got. It has its good and bad points, as you can see. The BF4 vram usage is a bad point, but it's on Dice/EA to fix. AMD did not write the Dice Battlefield 4 Mantle code path, or code their memory management implementation. AMD will not be able to go in and alter someone else's game code so im afraid it's up to Dice to fix it.
By all means feel free to rant and or be annoyed at the situation, not trying to deny you that. Just explaining where the problem lies and im afraid it's not with AMD.