If an airline carries a pax who has not the correct paperwork, the airline is responsible for returning him to the deparature point. Hence the airlines consider the time spent on checking pax documents as time well spent
I am well aware of this. My point is that if documents need checking, then do it properly once (and not so-so twice). There is obviously a concern that the person who checks in might not be the one that goes to the departure gate. Fair enough, then check all docs at the gate, not at the check-in desk or baggage drop. Saves everybody's time.