If, hypothetically, cruciferous vegetables were able to reduce estrogen to a level that is effective for hormone-driven cancers (and no, they are not), I would speculate that the side effects would be similar to the side effects of aromatase inhibitors, since most side effects are from the lack of estrogen.

There really doesn't seem to be much value in finding "natural" ways to lower estrogen. Either they don't work as well as meds, or presumably, in the unlikely event they do work, the side effects would be similar.

This is opinion, not from my doctor, but I have a close friend as well as an acquaintance who died using diet and other natural methods to combat cancer. Of course, everything helps, but I would eat cruciferous vegetables in addition to meds.