I'd disagree with you on that point, Keith.

Israeli can indeed be a noun, referring to a single inhabitant of the country, with Israelis as the plural. It is similar in that way to Pakistani and Iraqi.

On the other hand it can be an adjective, referring to the nationality of a thing, an institution or person. Thus you have an Israeli government, an Israeli school, or an Israeli child, in the same way you have a French government, school or child.

I hope that's adequately semantic and pedantic...