In many cases BGP does its job just fine at layer 3. But budgetary constraints and financial reality for the cost of really huge interconnection mean that a cut may result in a 100 Gbps PNI peering session between two ISPs filling up and flat-topping its traffic chart (very, very bad) when the traffic re-routes. One example is that as a result of today's events there was apparently major packet loss and congestion between HE and Comcast in the NYC area.

Or when traffic re-routes, a major ISP will temporarily congest its own intra-AS city-to-city links on a few key paths, for their own router-to-router interfaces.