There are two different things going on: the effects of the medicine in terms of what it does in the body to result in estrogen depletion and, secondly, the effects of estrogen depletion.

I haven't seen any studies that attribute all of the side effects of the aromatase inhibitors strictly to their result (the blockage of estrogen production) and none to how they work to achieve that. I guess we can't look at cases where women had hysterectomies, in comparison, as they don't result in zero estrogen production but it would be interesting to identify if an estrogen-less state has significant side effects beyond what is already known.