In 1789, it would have been inconceivable for the President to initiate a war, because he would have had to muster an army and the funds to pay for that army, and then march or sail them somewhere. That process took weeks or months, at least. A declaration of war to precede that action was not an unwieldy limit on the process, and was expected.
Now, with ICBMs, cruise missiles, strategic air forces, a ground force stationed all over and a navy that covers the globe, the President, purporting to use his power as commander in chief, can initiate what the Constitution would have envisioned to be a war on a moment's notice and without Congressional approval. The problem was ignored after WW2. During Vietnam, the anti-war movement made a stink about it, and Congress decided it needed to have a say in initiating wars. The War Powers Act was the result. It allows the President to initiate military conflicts, but if they escalate to a certain level, the President has to come to Congress for approval after a period of time. Congress' approval is the functional equivalent of a declaration of war.
The issue that could arise is what happens when the President, as Commander in Chief, initiates an action that creates a condition of war. For example, an attack on Iran, a sovereign nation, would generate a response, and we would be at war. Should the President not have an authorization from Congress before waging war on his own? (Note that Bush did get such authorization before Iraq, and Bush 41 also got authorization before the Gulf War.)
I think the Constitution requires an authorization before initiating action that will create a state of war. I don't think it's an optimum way to deal with threats in the modern world. You can't, for example, telegraph to the Iranians that you are going to attack them; you want to surprise them. But to be consistent, we have to follow the Constitution, even when we wish it was worded differently. If we want the President to be able to start wars on his own, we need an amendment. Otherwise, resolutions for authorization such as the Iraq War resolution, are the best compromise. The President can get authorization for a war that has not started yet, and he can then start it at a time of his choosing.
The President does not need authorization or approval of actions to defend the nation or our military. If we are attacked, a state of war exists that was declared by another entity against us. The President, as commander in chief, can and should defend us against a war declared by others. He just can't initiate a war. Congress can refuse to fund it if they disagree with the President.
In summary, the War Powers Act has worked pretty well since the 70s at allowing flexibility in a modern setting while staying true to the Constitution's structure. I don't know what problem this proposal is attempting to fix, but if the proposal gives Congress more oversight in the management of war, that would be crazy. As the Editor's Note states, Congress' role after war begins is to sit back and let the CinC fight it. They can pull funding if they are not happy.
So, it's daft to try to reinvent an outdated concept. They're just a bunch of Bush-haters creating a system they hope would have thwarted him from going into Iraq. But Congress was asked to vote on that and said yes. Oh, never mind!