It's my understanding that the restrictions on the actions of a democracy come in this instance from the fact that it is, to some degree, accountable to it's citizens. Therefore when you cite how the US "does what it wants" etc this doesn't really invalidate the point because it is accountable to Americans, not to the rest of the world, so if Americans want something, then it is not restrained in doing this. I think as well that a closer study of Israel would reveal it to be very constrained by public opinion; the early end to the most recent Lebanon War is generally the go-to example in this case.
There are also other reasons why neoconservatives believe that a world of democracies is safer for America. Anti-Americanism (and anti-Israel'ism') is seen as something that is fueled by repressive regimes who need to distract their populaces from their own oppression and poverty. Thus if these countries were free, democratic, and prosperous, there would be less hate for America and Israel.