In 2016, a single misconfigured DNS record took down a major cloud provider’s load balancer for four hours. During that time, every application behind it was unreachable. The load balancer had been the indirection layer between the internet and thousands of servers — the one component whose failure made every other component irrelevant.
Load balancing solves a straightforward problem: you have more requests than one server can handle, and you have multiple servers. Distribute the requests. The solution is straightforward; the failure modes are not. A load balancer that distributes requests evenly to servers that are already failing makes things worse, not better. A load balancer that is itself a single point of failure defeats the purpose of having multiple servers.