I worked at WhatsApp until 2019; I don't remember any disaster plans where taking everything down was an option (although I'm sure they exist), but dropping BGP sessions is probably not the best way to do it, because it's hard to reverse and hard to inspect the system without BGP.

Over in WA land, we'd probably just kill all the frontend servers if needed. For all of FB infrastructure, killing all the loadbalancers would probably work, and also the outgoing proxy hosts, as appropriate. No need to mess with DNS or BGP.