Perhaps it's time for a new definition.

Unskilled labor is what you call someone who merely has skills that most everyone else has.

If it's not scarce, why pay extra?

Skills matter. The unemployment rate for US workers without a college education is almost triple that for those with one. Even the college rate is still too high, though.  On the other hand, the unemployment rate for skilled neurosurgeons, talented database designers and motivated recombinant DNA biologists is essentially zero, despite the high pay in all three fields.

Unskilled now means not-specially skilled.