Rather than get into a lot of details, here's some excellent starting points:

[1] Google Cloud networking in depth: Cloud Load Balancing desconstructed - https://cloud.google.com/blog/products/networking/google-clo...

[2] What is AWS Global Accelerator: https://docs.aws.amazon.com/global-accelerator/latest/dg/wha...

[3] Tumblr: Hashing Your Way To Handling 23,000 Blog Requests Per Second: http://highscalability.com/blog/2014/8/4/tumblr-hashing-your...

[4] Load Balancing without Load Balancers: https://blog.cloudflare.com/cloudflares-architecture-elimina...

Yes, I understand how anycast works (I work for an anycast based CDN).

The issue is that you can't do percentage based routing with anycast... in fact, you can ONLY do shortest hop routing with anycast (at least for WAN anycast). That means that, while different edge networks can go to a different datacenter, every individual edge network will hit only a single datacenter.

The key issue is that anycast is a very blunt tool. You are relying on your BGP announcements to route traffic, but you aren't actually in control of where a particular request goes.

Rather easily. There are routing protocols designed for such things. Far more reliable than trying to hijack DNS for load balancing.

Indeed the root DNS servers are not a single server but pools of geographically distributed servers via anycast.

Anycast doesn't support percentage based load balancing unless you control all the hops between client and server, which is almost never the case if you are serving the public.

Every request that comes from the same network is going to be routed the same way. Anycast works great for regional load balancing in general, but it doesn't work for subdividing individual networks.