I could be wrong/this is probably ignorant to say but I'm pretty sure we don't want "full employment".
The fuller employment, the more supply there is for jobs of all wage groups (low, medium, high, etc.)
Employers were having a hard time finding people who wanted to work during COVID for a variety of reasons. This lead to a good think for workers who did want to work: $12/hr jobs became $17/hr (rough example) due to low supply, high demand.
The fuller employment, the less need employers have to compete for workers on wages.
Just a thought...