Achangel62 - are you saying that these "factions" did want the Reds gone but not as quickly or fully as it happened in Changes? It seems counter-intuitive. If you want them gone at all then you want them wiped out. Why would the Black Council or whoever want to only kill them slowly or cripple them? Same with Mab or Vadderung (who benefited from the destruction of the Reds).
My thoughts are that it might have been the difference between a bombing run and a controlled demolition. Removing them the way that happened as fast and direct as ended up occurring meant that there was now a hole to fill and if they didn't have agents set up either some other faction could fill that void or their people might be able to take it but might not be fully prepared. They also may have hoped to further weaken the white council with having them keep fighting and struggling. The time honored tradition of 'let's you and him fight"
Also a longer fight might mean that they could make pacts and deals, get information, tools or other resources from an increasingly desperate red court. They also might be able to find agents here and there that they could set up to handle other tasks.