Also, wouldn't a DNS provider or hosting service be able to "beef up" to handle the traffic from a DDoS? Especially if it's a nice one, it seems like something you'd expect from them.
And yes, there are ways to essentially start throwing servers online and yes companies do it. The problem is it becomes obscenely expensive — if you do this and go bankrupt, again, the DDOS has succeeded. It's actually somewhat problematic to do it automatically for exactly that reason. What if you preferred to just take your service offline until you could investigate enough to stop the attack instead of pay hundreds of thousands per day in server costs?
This is why DDOSs are a bitch!
Edit: Also worth noting, it's probably for this reason that Github is still accessible: throwing servers online and eating the cost.