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.