Your second metaphor ain't correct. Google and FB's normal way of executing doesn't consist in sending regular trafic to a bicycle (server) until it crashes and then re-dispatching that legit trafic to non-crashed servers.

Sure a server does crash once in a while but it's not because they purposefuly did overload it.

The DDoS attempt trafic is dispatched left and right just like regular trafic and doesn't affect the normal behavior.

It's more like the single truck can hit any of the 1000000 flying bycicles.

: )