And why should we not manage for the forest to regenerate with the same timber species that are there now?
Because our forests that exist today developed under entirely different conditions than exist today. The harvest rate in 1900 was not 1%/yr. as it is today. Forest fires burned uncontrolled which eliminated many shade tolerant species like red and striped maple. there were no invasive species in 1900 and there were no invasive insects like the gypsy moth ,leaf rollers and we didn't have the tree diseases we have today.
furthermore, replacing the existing canopy is in opposition to mother natures grand plan which means that shade tolerant species that develop under a closed canopy replace the existing canopy of less shade tolerant species.