Does anything in the Constitution give Congress the power to act as commander in chief? If not, then there's your answer.
As for the power to "start a war whenever it suits them", they are explicitly given that power.
LOL, so you actually are claiming that Congress can in deed act as Commander-in-Chief since the Constitution gives Congress the power to declare war and that, as you would say, is a traditional and historical "default" power of the office of Commander-in-Chief!
Under the Articles of Confederation, perhaps, but not under our Constitution. While Congress was granted the power to declare war, it is only the President who has the power to make war. The framers specifically debated this very issue and decided against allowing Congress the power to make war, and instead, gave that power to the President, through the office of Commander-in-Chief.