I cant speak for Mill only speculate but I think I can answer for myself.
To me if there were such a thing it might hinder my ability to feel pleasantness. It seems that we define great pleasure in terms of it's opposite. So if you diminish the opposite of pleasure long enough then that pleasure too will also diminish.
Some might argue that simply can not be. Look at pain killers for chronic pain? Would you rather have the chronic pain just so you can keep fresh your understanding of pleasure? Well I think if you deaden one you are probably deadening the other equally. Maybe that's just my ignorance but it seems to be that way.