Bealine's got it in one. There was a time when airlines could easily rush passengers to the gate, for the most part those days are long past, what with security and slots etc.
We also have the problem of inconsiderate passengers who bear no thought for their travelling companions( I'm not suggesting you are Little Chief) but, I've known late passengers who have been checked in after closure, told to 'run' to the gate or they'll miss it, yet still find time time to rush through the Duty/Tax Free, stand at the sales desk get their purchase, and stroll to the gate only to delay the flight.
In truth it isn't the check in staff you should asking, it's the other passengers who run the risk of a missed slot and the subsequent delay.
Perhaps we need an article explaining all this in the In Flight mag SectorBabe.