In general the be all and end all in the aviation industry is that aircraft needs to be off stand on time. Airlines in general like to protect their on-time schedule performance as it is now published.
When aircraft don't go on time then everyone needs to know the reason especially if you work for a 3rd party agent handling the flight.
As modernised aircraft start to be entered into service with ACARS installed they monitor and send to airline operations the times of doors closed, pushback and airborne times. This halts the descretion of calling a flight of time confirmed with Captain allthough really it's 5 minutes late.
3rd Party agents can also be fined for taking a number of handling delays which including late acceptance of passengers. (unless at captain special request).
The fine line is who is telling the truth and who isn't? With -20 & -30 check-ins along with internet check-in passengers. Passengers are cutting it fine and leaving minimum time to turn up at the airport.
I would prefer that discretion could be used however the pressures for on-time performance and having to explain your actions along with a possible record on personel files will deter it. Not everyone is honest.
The good old days where nobody would question a delay are well over.