Re: iddat
I have never heard the stay in home part but anyway.
Some argue that women have more emotions and need time to get over their ex. or late husband, but I don't think that is the main reason.
The main reason is to be sure she is not pregnent. These days there are tests (which themselves put a disclaimer that it is not fool proof) that will tell you in a day but then Islam is not only for those living in the west who can afford it all.