@Ltryptophan , the bigger problem, as I understand it, is damage below the cap, in what’s left of the original blowout preventer, and in the well bore itself, which passes through thousands of feet of rock. Think of pinching off a garden hose. You stop water from flowing out of the end, but if there are weak spots or small holes in the hose itself, you risk rupturing it and having a flow that you can no longer control.
The cap can serve as either a collection or containment system. As a containment system, we would rely on it to stop the flow of oil altogether until the relief well is done. That would be ideal, but you run the risk of a leak in the system below it, a risk of the cap blowing off, or in the worst case, a buildup of pressure in the well bore that would blow out near the relief well. It would be better to open up the cap than to have those things happen, if you can capture all or most of the oil and siphon it to the surface.