It can't be much simpler.
It's not a bad idea (although it hasn't been the case for every war at least since Jefferson), congress would probably still be pointing fingers (I believe the war itself would have been declared) but they would look a lot more foolish.
In the extreme case if the US were suđenly invaded by a foreign army the president can counterattack without waiting for Congress to Declare War on the invading army. Declaration of war means just what it says, nothing more. You do not want Congress to declare war except in conditions that at least approach the severity of WW II. A Declaration of War is, essentially a suspension of normal Constitutional protections and relationshipsthat that allows the executive to take over the economy to direct the entire output toward the prosecution of the war. We have not been involved in any such war since 1945.
The president has the power to go to war outside the US any which way he desires but he has to get Congress to pay for it. Congress is still in control. Congress can't stop the president from sending the troops somewhere but the action is limited to what can be accomplished before the money runs out. Congress ended the war in Viet Nam and got a few million extra people killed because Congress cut off the money to operate.