FWIW, that's what happens for large customers too, from my past experience. Someone aims the DDoS cannon at one of our webservers [1], and if the traffic is above the threshold, that server's IP gets blackholed for a while. As a large customer, you
do get to have some input into the thresholds, and how long the blackholes are, and to definitely have traffic blackholed rather than put through some crazy filtering apparatus that adds so much latency it'd be better to drop everything.
OTOH, we always had at least 4 webservers, so if just one got blackholed, no big deal, update DNS so most of the real users make it to the available servers, most of the abusers will keep hitting the blackholed server and not move on. If your abusers aren't run of the mill script kiddies using a rent-a-ddos service, it's more difficult.
[1] it's almost always the webservers, not the servers that do real work