It's important to understand that the value of the unemployment rate is not the absolute number but its change over time.
We also have other metrics published alongside the unemployment rate, like labor participation.
We all seem to be admitting that it's a bad, misleading statistic. So why are we so committed to keeping it around forever? Why not change the definition?
People say "for historical comparison", but what's the point of a historical comparison of a statistic that we all admit now is bad and misleading?
The fact that something has always been done a certain way is no justification for continuing to do it, especially if the initial decision was misguided in some way.
It's much more misleading to suggest that the people not included in the unemployment rate are the "hopeless" since it includes children, the retired, and those unable to work.