This is the key insight: it's not a question of better or worse security. Airport screening doesn't enhance security. This can even be experimentally measured. Bottles of liquid get screened reliably while weapons don't get detected because it's rare for a weapon to pass through the baggage screening machine. The correct response to a lose lose situation like that is to minimize the cost and friction until someday it's announced that a magical technology can do mass walk-through "screenings," and we can stop paying the shampoo bottle screeners.
I think I would prefer more accountability, if a private firm can do that, than I see no issue.