Shared earths is an issue regarding how the voltage rectifier works. The GG stator is a simple single phase AC system. The windings are in series with the yellow wire being ~80% tap and the white wire being a 100% tap. The bottom end of the windings is grounded to the engine/frame.
Simple explanations regarding voltage rectifiers:
https://www.rohm.com/electronics-bas.../rectification
https://www.ccontrols.com/enews/2018/0518story2.htm
On a GG the yellow wire is regulated to ~14 volts AC relative to ground. This is the most basic method for lighting. The filament in a bulb works fine whether it gets AC or DC voltage. The white is not used since the regulator would have to work that much harder to clip the excess voltage.
On the newer machines with estart, the white wire is used to feed the rectifier. The AC stator voltage on the white wire is rectified to ~14 volts DC.
Since the GG system shares the stator ground and the battery ground it uses a half-wave rectifier. This removes half the sine wave and the higher voltage on the white wire helps to make up for this loss. The lumpy output (more like a pulsing DC voltage) is leveled out by the battery.
A full wave rectifier is more efficient but requires isolation. Since the battery is grounded to make the starter system simple, the stator ground must be removed from the engine/frame ground. This is often called "floating the ground" and requires a modification of the stator. The bottom end of the windings is changed to only connect to a new additional wire. AC output occurs on the white wire and the new wire. This feeds into your full wave rectifier. There is still a reduced AC voltage between the yellow wire and the new wire but it is not used. This floating of the stator ground allows for a grounded output of the rectifier (required by the starter motor).
So why do we want DC voltage? Battery charging is the main reason. So if you do not add a starter, you really don't need a battery. Some juristictions may require a method for the lights to be on without the engine running, so that needs a battery. Horns and flasher relays also want DC voltage. Most everyone adds a battery since it's easy to do.
The simplest way to set up an electrical system is to leave the stator grounded and have the rectifier output ungrounded. Take this ungrounded DC power to just the items that need it. It will be there for all your devices EXCEPTING a starter motor. This mixed system will work fine if you hook it up properly.