It seems you don't quite understand. What you mentioned will still be studied and analyzed. The other is just a simple formula used in demographics to determine the future costs of public programs and how they will be paid. Roght now the boomers are going to need a lot of young people there to pay for their pensions, medical expenses and so forth. Will these expenses be covered by those who are working and paying taxes is an important question. This research also has implications in immigration also.
They are. And they are studied. Expanding the definition of unemployed would actually hurt researching those issues. As it is, we can look at who is working, who is looking for work, who might start looking for work, who doesn't want to work etc. That would be a lot harder to do if you simply grouped everyone together as "unemployed."