It is obvious those two are very different situations. I'm not sure I understand your point. Yeah, nobody will be bothered by a short 15 minute DDoS attack. I prolly wouldn't even notice it unless I'm actively checking the logs. Sure, nobody is going to be bothered by that. But what if someone's DDoSing persistently with a purpose? Maybe they're just pissed at you.
My point is... a sustained DDoS attack will just make your host drop you. So one situation directly leads to another and you are forced to deal with both situations, like it or not.