The current system where the airport is making decisions about dismissing or delaying an aircraft is unrealistic.
Airlines have to keep their planes on schedule. Boarding gates should close 10-15 minutes before scheduled departure (more for flights from a remote stand). If people are late to the gate the plane just leaves because it has to remain on schedule (as far as possible) .
However if a requested service isn’t provided, particularly refuelling (when it’s introduced de-icing should also be a no-go item) but other services as well, the plane should stay put and you shouldn’t be able to send it away because a plane without enough fuel, or ice on it’s wings, isn’t going anywhere.