Normally you Anycast DNS only, and then use DNS load balancing (of IPs) to load balance physical load balancers (which are themselves sharing IPs on subnets and doing high availability stuff) in front of banks of servers.

You probably implement Geo, health, and load based optimization in the DNS layer and also in the physical load balancers. A single host out of ~30 dying at Site A doesn't affect how the DNS load balancing responds, but a critical number does.

Due to broken DNS implementations in the wild, you ideally keep your per-site load balancers up in as many situations as possible (even if load must be shed, you keep core network and load balancers up) and redirect traffic from there to other sites.

For larger sites, the big choice is running a single AS global network where IPs can move between datacenters vs. running each datacenter as a separate network. Advantages and disadvantages to each.

The big disadvantage of all of this is you're now spending a few million a month on salaries, infrastructure (various PoPs, network gear, etc.) before you've bought a single server or served a single page. Not so lean.