There is absolutely no purpose other than propagandistic for the percentage commonly referred to as "unemployment" with no other qualifiers. That number's only purpose is to start dropping a short time after an unemployment shock whether or not any jobs were actually added to the economy.

The other numbers aren't to give a "broad picture" of the labor market, they're to give the entire picture of the labor market. "Unemployment" contributes nothing. At the time of a shock it echos other metrics, and after a pause of a few months it announces that whatever the administration announced its reaction to the shock would be is starting to work, no matter what the other numbers say.