There are three things. One is that NATO can't expand to every country on earth; we can only expand in Europe. That's a charter restriction. We have partnerships with many other countries, but certainly it won't expand.
Second, NATO doesn't have the money, or the mandate, or the ambition to do what the UN does. We only do security, and the UN does everything.
The third thing I would say is that to a large extent you're right; NATO has been the muscle for the United Nations. Having worked on UN peacekeeping when I was at DND, I think we should be glad about that, because the UN cannot handle 95% of the things that are given to it to handle. If we relied only on the UN system and blue helmet peacekeepers, they would never be able to manage it.
I would direct your constituents to what Ban Ki-moon has said about the NATO intervention in Libya. He said, “We've saved countless lives” on the UN mandate. They could never have done it.
So I think there is an upside for both organizations.