The tier 1 & 2 ISPs I've worked with have a blackhole BGP community. https://www.rfc-editor.org/rfc/rfc7999.html
Normally for DDoS migitation, you blackhole on your normal ISP, and you simultaniously advertise on the mitigator. The mitigator scrubs the traffic and sends the clean stuff over a private session back to you.
If you just black hole and move on, yes that's a lose. However many ISPs will, because the quick reaction holds the most value for them.