The war could be won not using the Colossus, the problem was that the destruction of most of the 6th fleet forced the GTVA's hand on the matter and since they were already engaging the Shivans, that conflict needed to end as swiftly as possible. It's basic strategy, never fight a war on two fronts but as we all know GTVA command doesnt know anything.
About the Hecate, the idea is good but the design isnt, a dedicated C&C and fighter carriyng capability is always good but they should have designed the ship with more defensive armament, against capital ships and small craft, even if its not meant to be at the front line it should be able to stand up by itself, something that the Hecate fails to do.