Erwin - Your theory assumes that the electricity in the battery is disappearing somewhere.

Why does the alternator have to generate any more electricity than the car uses?

Consider

Condition 1 - Car uses less electricity than the alternator produces - the battery reaches full charge and the excess is controlled by the regulator.

Condition 2 - Car uses more electricity than the alternator produces - the battery gradually loses its charge.

An elecrical system that operates in condition 1 has a battery fully charged all the time. A car that operates in condition 2 some of the time profits from having a bigger battery to tide it over until condition 1 time is amassed. A car that operates too much in condition 2 goes dead eventually, the battery size does not really matter, big or small the battery dies.

Of course the real world is complex - battery drain when the car is not in use, the deficit produced when you crank the starter, use an accessory, leave the door open, etc, temperature variations and so forth.
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3 8s & 2 7s 725,000 miles total