Sometimes in my work I have to deal with the portuguese slots coordinator and I know it's hard to satisfy the airline requests, sometimes just impossible but they have software to do that job and just have to accept, recuse, delete or give an alternative slot.
But talking about operational demands, aircrafts can land without slots coordinators.
After ATC I would put the ground staff who offers the handling services to airlines.
Just imagine that there is nobody to manouver the staircase near the aircraft so that the passengers can leave it. Yes, this is an exagerated example but is to show the importance of ground staff.
Other I remeber now is the meteo service, also very important.
Luis, Faro, Portugal