They could do that. Assuming that they have other servers to assign. They'd also have to remember to set the lease time short enough so that when the problem goes away, everyone is switched back fast enough.
Also, for people using routers, they'd have to reset the router, and reboot their computer. Rebooting their computers would just get the same DNS servers being given out by the router. And while just resetting would change the DNS information in the router, it would still need to be served to computer, which would either need to be rebooted, or release/renew the lease.
But again, that all depends upon having backup servers available. It would be my guess that if more than one DNS server goes down at the same time, the problem is more likely to be a problem with communications to/from the data center where the DNS servers are located. So they not only would need to have back-up servers available, they'd need to be located at another data center.
Also, you need a global way of changing the information to all the accounts, and that information would need to be pushed-out to the regional data centers where the DNS servers are located. And if there's a problem with the central data center, well, making that happen would be a problem as well.
So while you're theoretically correct, the practical application of that solution is far more difficult than it sounds. And implementing a work-around usually takes resources away from fixing the actual problem as well.