i took a look at a '81 wiring diagram.. Headlight and horn are run directly off one of the two lighting coils.. they are not connected to the battery in any way. Nor is their power rectified so it's AC and voltage varies with RPM..
The battery is just an appendage, added as if as an after thought.. simply spliced into the harness between the SCR and ground. So, everything should work without the battery. Since battery power only supplements the other accessories, engine RPM would be related to power delivery to those other accessories.
This bike's system is not over complicated.. it's over simplified .. unsophisticated. My guess is the addition of a battery allowed them to save money somehow .. perhaps by using smaller or weaker designed components in the magneto..