Their constitution could also be seen as a symbol of shame. A constant reminder that they lost in a previous war, and were imposed limitations no other country has to deal with.
I don't see the problem with turning the JSDF into an official army. They aren't going to suddenly turn expansionist, and there are cases where armed intervention on foreign soil is the decent thing to do.
Besides, wanting Japan to be unable to act outside it's borders, while also wanting western nations and the UN to do something about ISIS, sound a bit hypocritical to me.