Since you read the Lighting whitepaper, you know that an uncongested base-layer is assumed. The paper suggests something like 133MB blocks at scale.
The same volume without lightning would require blocks that were terabytes, which is obviously unworkable at the current state of technology.
A "black swan" event like a major lightning hub going down may force more channel closings than the network (as currently implemented) has time to process before time-out.
The LN simply does not work if the base layer is congested.