First off welcome to the forums, i find it very courageous of you to open us to strangers so soon after becoming part of this forum.
That said, i agree with you when you said that this is her issue to deal with. Unfortunately it's very difficult to see the person you care about go through this when essentially you can't help them. I don't find anything wrong with you telling him that you feel he should deal with the ex "once and for all", in fact it's important to tell him how you feel.
In the end it's up to him to decide to do this or not. i would suggest that you don't take it personally if he doesn't heed your advice, as it might be something he needs to figure out on his own.
then again that's just my take on it, and i'm sure there are wiser people here that will give better advice.