Ignoring packets is cheap, but if your connection is unable to handle the shearsheer volume of traffic per second then you're going to fall down hard. The only answer at that point is to filter traffic upstream of you. Because things are distributed and high performance routers really don't like consulting a large routing table just to play whack-a-mole on which hosts to drop, that can get unwieldilyunwieldy.
That last part is what makes a DDoS so effective: that it's hard to reroute traffic upstream. CloudflareCloudFlare makes a business out of having enough bandwidth to absorb all the traffic and deal with it without having to filter upstream at providers.