Yep,Hitler was elected democratically alright,but he dismantled Germany's democratic institutions before doing the things that made him (in)famous.There is a world of difference from being elected democratically & running a functioning democracy.
I know, however If there had been next elections, Germans would probably have chosen Adolf again, at least until 44.
My point is that democracy doesn't guarantee peace. Democracy may works in Iraq and would work probably also in Iran, but the result of democracy in Saudi Arabia would be worse than current situation.
BTW I don't If Israelis should give up nukes or not - I'm just not very interested in this issue, but this position of State Department is just a part of diplomacy - US government sometimes just has to say something like this If wants to have opportunity to be a negotiator in Israeli-Palestinian conflicts. Aid worth billions would be cut off If US government really wanted to kick Israelis.