As for why people use APIs for configuring things, it's because infrastructure changes frequently enough that encoding it in a static file isn't practical. Imagine you are rolling out a new software release. There are 100 replicas. You could start up a new replica, see if it passes health checks, edit the haproxy config to configure that as an endpoint, wait for haproxy to start sending it traffic, check that it's working, edit the config file again to remove the old version's replica, wait for haproxy to acknowledge that change, shut down the old replica... and finally do that again 99 more times. Nobody wants to do that, so there's an API to inform your frontend load balancer of where your workers are. When it needs some endpoints, you tell it.

I guess an even better example is TLS certificates. They expire every 3 months. What do you do when a new one is released? Drain traffic from one load balancer, copy the certificate and key over, wait for the load balancer to restart, and then undrain traffic? No, that's a huge pain. You just have your load balancer connect to your secret discovery service and have the same program the renews the certificate send your load balancers the new certificate. Then you don't have to drain; when a new connection comes in, you present the new certificate.

All these config APIs make it possible to operate software at scale. You probably don't need it for your personal website. But you could probably eschew servers entirely and just nc -l on port 80 and type the response in your terminal when a request comes in and still have a mostly-working website.