I've had my doc make the same suggestion. The rationale is that the IUD delivers the medication with less likelihood of the side-effects that can come from delivering the drug systemically.
I think doctors want to go to the silver bullet first, because relatively few patients have a moral issue with using an IUD under these circumstances and a lot of patients do not want to work their way through other options. This is the gist I got talking to my own physician. Even if the contraceptive issue were not there, though, I would not be comfortable with the possibility of perforation. The ob/gyns see the problem as unlikely; the emergency medicine people seem to be more against them, presumably because they see only the perforations and not the people who had no problem. Kind of like motorcycles, I guess. I know far more emergency medicine people, so it is unlikely I will ever have either an IUD or a motorcycle.
I decided that the side-effects of the hormone included all the things I hate about my period, and since endometriosis and cancer were ruled out, I decided to live with the symptoms for awhile longer, because I got checked out before my symptoms had taken quite the toll that your wife has had to undergo. It happens that mine resolved on their own.
If that had not happened, I would have started with other possible treatments and gone with the option that had the unintended side-effect of contraception as a last resort. Certainly I'd leave the one with the small chance of perforation as the very last resort. As others have suggested, the iron-deficiency can be addressed as its own issue. Still, from experience I also understand that the fact of enduring heavy bleeding is tiring all by itself, even when it does not bring the iron levels down. IOW, if she feels that the tiredness is not just about the iron deficiency, I can say my experience is the same.
That is my experience only.* It is very important that she make her decision based on what doctors tell her about her condition.* I'm only chiming in to give an example of someone in similar circumstances that she can decide is similar to her,* if she sees fit*. Her condition could be exactly like mine on paper, and yet her sense of it could be very different. Her sense of it is very important, too.
If the IUD is what she is stuck with in the end, she should not punish herself about having to take on an unintended side-effect, even if her private sentiment is that she would rather not have any more children. If she would make the same choice even if she very much did want to have children, then she can let that side of the equation go. You may have to treat the problem, if it is affecting your ability to serve in the other capacities to which you are called, even if it precludes the capacity you would choose for yourself. Whatver else she does, try to talk her out of Catch-22 self-doubts. Rather, let her do the best she can, and encourage her to have peace that it is the best she knows to do with the information she has found after seeking in good faith. That is all God ever asks.