The ocean crust isn’t thick enough. The formation is over 2 miles beneath the sea floor, such a cavern would extend down into the mantle.
That's always been my take also - the ocean basins are basalt and the channel/cavern thesis doesn't compute. But then again there's a hell of a lot of oil coming from way down there, there is indeed a lot of outrageous pressure, and my wife says I've been wrong before.