If you were a fire chief how much would you trust an initial report that there are no passengers in an aircraft? And if it turned out that the aircraft was destroyed unnecessarily, or the gate put out of commission long-term due to the lack of an adequate response, or the burning aircraft set fire to adjacent aircraft... you'd wish that you'd sent the whole fire crew.
If you doubled the size of the fire crew, would this prevent you from sending all of them to the same incident? It would be difficult to make the decision not to do so, if they were available.
The decision to send the whole crew seems to me the only reasonable one. After they had started tending to the fire and had more of a view as to how serious it was, perhaps they could have been taken back and the airport reopened sooner. To me this seems the only possible area for improvement.