Here's a quick graphic of the path for the 9 amps to the headlights.
View attachment 1715843036
With relays, that path will see only a fraction of an amp from the headlights being turned on.
Instead the current will flow from the alternator to the headlamps only going through the relay and one breaker or fuse. Being a shorter path, with larger wires and less connections, the lights will also likely be brighter if using a sealed beam or H4 type headlamp. If you are using LED headlamps, then the advantage will likely be much less. That would be somethng to discuss with Stern.