I would think that if the EZY was overly pushy it was because he was on a slot and if you miss your slot the next one is usually in excess of an hour away.
And what makes you think ATC don't take this into account. We know the slots (indeed, they're passed to the aircraft along with the clearance) and we update the aircraft as and when they change. With that in mind we have a window (-5/+10 mins) on a slot within which to depart the aircraft.
If a pilot is going to miss their slot I can assure you - it's normally down to reasons OTHER than ATC.