Did the Einzbers hire Kiritsugu to represent them and wish for the Root Or did they know that his intention was to wish for "world peace"?

I was confused when Iri said in ep 20 of Fate Zero that if Kiritsugu's dream comes true then the 4th war would be the last one and Illya wouldn't need to be sacrificed for the next war's grail. But don't the big 3 mage families only care about reaching the root ? world peace becoming a thing or not. I was under the impression that reaching the root is it's own wish, since it requires the master to have his own servant commit suicide via a command seal, as it was explained by Kirei to Gilgamesh in ep 17. And doesn't that mean that the servants never get to make a wish, even though it's established that most of them are seeking the grail for a personal wish too ?  How many wishes does the grail grant ? Is reaching the root considered a wish. Do servants actually get to have their own seperate wish granted alongside their masters, or was that a lie fabricated to make the servants fight.