"Shouldn't the packets get rerouted if a particular link is down?" In a perfect world, yes it must be rerouted.
In real world ISP have peering contract between them, they usually share some amount of bandwidth for free ( balanced usages form two neighborhood, etc ... ) but charge for the extra ( you use my infrastructure and it have a cost ).
So most of the ISP and large network infrastructure provider ( backbone, undersea cable, etc ..) will not forward rerouted packet for free.
Pro. it's encourage big ISP to be directly connect to each other. that mean cheap "regional" bandwidth for the ISP and an high density network.
Con. It's make the inter continental/regional traffic expensive and unwanted. That one of the reasons ISP hate P2P traffic. Minor player are isolated and vulnerable, their are not interesting for big player ( few bad peering contract ).