the alternator output voltage isnt always constant.
In a standard lead acid 12/24V motor vehicle battery system (identical to the GA aircraft version) the purpose of the voltage regulator is to maintain a constant 14/28V voltage across the battery.
The battery then takes care of its own charging, by drawing a current which is according to the difference between the charging voltage (14 or 28V) and its internal cell voltage (typically 12/24V).
I am an electronics hardware/software designer and used to design solid state regulators for motorbikes in the 1970s, back in the days when the regulator was essentially a relay with a vibrating contact and thus lasted somewhere south of no time at all.
It's a very simple system.
Doing it so that the system runs without a battery present (i.e. the alternator delivers a relatively smooth 14/28V) is more of a challenge and I don't think anybody bothers. It can be done by controlling the field current with a fast feedback loop, but may possibly require a customised alternator with a low inductance field winding. This is what GAMI claim to have done. It would be a neat thing to have because it would not matter if the battery became disconnected in flight, etc.
Though an observed meter may show a 'steady 28 volts from your alternator/regulator, an oscilloscope may well show many high transient spikes.
It's these the battery [and sometimes a capacitor] flatten.
Without them in the circuit the electronics may suffer.
Exactly. A scope would certainly show the ripple, at a frequency of 6 x alternator revs.