The configuration file allows to reconfigure at once in an atomic manner. The configuration is also verified before reconfiguring and can be aborted if it's not runnable.

HTTP offers none of this. No atomicity and no consistency of the full configuration. Want to edit a service or maybe alter some hosts? Better hope it's already setup as expected before editing and you're doing all the right calls in the right order and they all succeed. You will have to write the hell of a state machine to ensure to get to the expected state.

The only sane use case for live-changes is enabling/disabling a server, which is necessary to perform rolling maintenance or blue-green deployment.