Do airlines have an ATC schedule they have to adhere to? Do airlines have to include a departure window when they file their flight plan, or communicate it otherwise?

As many people know, airlines operate on schedules, but I think we all have seen delayed flights, sometimes for 10 mins, sometimes for a couple of hours. However, that is the airline and the customer's problem. Do ATC or the Management at the airport have a departure window though, so if the plane does not depart in between these times; and it is not the airport's fault, they will not let the plane depart, or fine them?
The estimated off block time, EOBT, which is the time at which the flight is planned to leave the gate at the departure airport, has a validity of +/-15 minutes. If the plane is not able to depart within this window, the company must send a new ATC flightplan with an updated EOBT.

In some cases a calculated takeoff time, CTOT, is issued to a flight. This is the exact time the plane must begin its takeoff roll. It is given based on airspace or airport congestion along the planned route of the flight, to prevent overload in individual ATC sectors. The flight must begin its takeoff roll within -5/+10 minutes of the CTOT. If unable to comply, a new CTOT must be requested.