You can only deice in locations where the runoff can be collected and processed. You can't let the runoff go into the water table. At some airports that includes some gates. At many airports it does not.

Even when you can deice at the gate that can cause other problems. The fluid is thick, slippery, and runs off slowly. The ramp crews and equipment have to continue to work at that gate for subsequent flights. There is often little room for the deice trucks in the gate area. During icing conditions with the associated delays, there is often another flight waiting for the gate to vacate so they can park. If the frozen precipitation is ongoing, the hold-over times (from the start of the final anti-ice application until takeoff) is short so the time from deicing to takeoff is limited. When there i a lot of deicing ongoing it is more efficient to have all the deicing equipment in a central location so that each crew can deice more aircraft.

For all these reasons, the specifics of the deicing procedure will vary from airport to airport and even at the same airport as the severity of the weather conditions increase.