Why are all the people who live at the House of the Old so eager to be released?
I would say that there are a couple of reasons.
First of all, no one actually knows what "release" means. All they really know about it is that you have a really nice ceremony done for you. Then you get released and who knows what happens. So it probably seems like a nice thing.
Second, I imagine the old people feel sort of useless there. They don't really have anything useful to do. They are treated like kids (even as far as having the wand used on them). So I would imagine that they do not feel all that motivated to keep on with the kind of life they are living. So they might welcome a change, especially when they don't know that that change is really death.
In the house of old in the book The Giver the people are treated like they no longer really matter. They are kept there like children and even disciplined like the children. Some are not even that old when they are moved into the residence. They have been conditioned to believe that once hey have raised the children up and completed their assigned duties in life, they are not worth anything to the society. They are no longer given respect as people can see them naked pretty openly.
It would only stand to reason that the promise of a happy "release" which has been ingrained in them as being something wonderful, would be something that they would desire. They have no idea that their death would be what release means.