Just to be pedantic. :- In automotive applications, Alternators come in "battery-sensed" and "machine-sensed" versions.....the net result is the same, the BATTERY should be maintained at a nominal 14.2 volts,for a "12V" lead-acid battery.
The posher alty's also have temperature-compensation built in,
The machine is set to the nominal voltage as a compromise,- to maintain a charge and replace a "surface-charge" (discharged by starting), yet not to overcharge, which would "boil" off the distilled-water part of the sulphuric-acid solution which forms the L/A battery's electrolyte.
Often, people are baffled,when , after starting with a flat /depleted battery, a short run restores it to full vigour,However, after a few hours' non-use, the surface-charge has dissipated and the battery is again depleted.
That is why an external charger is advised ,to deep-charge a battery and maintain it with a "float-charge"....cheap chargers will poke in a full charge,their output being reduced by the battery's rising voltage opposing the charger,-but an unregulated charger will gaily carry on "stoking" a battery and electrolyse the water (hence the warnings about not smoking and switching-off before disconnecting ) the liberated hydrogen and oxygen can give a hell of a bang and casing and acid get everywhere
Work it out, folks....a 36 AH battery will, at peak,deliver that amount...BUT USUALLY AT THE 12-HOUR RATE.....that means that THEORETICALLY a mint system would give a continuous 3 amps for 12 hours....we already established the load is typically~40 amps....so you'd be very lucky to get 30 minutes from alty -failure to loss of power due to voltage-drop.
As others stated, the battery acts as a small "buffer-tank" to provide starting energy and even-out the load on the alty.
Petrol V diesel !....the magneto is completely self-contained. engine will run without any external power.
Diesels commonly use a fuel-shutoff solenoid to switch off.....when the volts are inadequate,the valve closes and the donk starves. Modern Diesels also use electronics for injection, as opposed to the old mechanical injector-pumps with the pull-wire to stop.---same problems with lack of volts....the brain dies and kills the donk.