VERY basically put, alternators work on the concept of comparing a circuit in the car to what voltage it's putting out, always trying to keep them equal to its setting. In the case of a 12V car, that's about 13.5 volts. If that secondary circuit, the field circuit, gets low on voltage the alternator puts out more; if it gets high, less.

Therefore, with an alternator, if you cut off the battery only then as the field circuit voltage drops the alternator tries to out out more and more voltage. Eventually the field circuit voltage will drops too low and the alternator goes offline, but it's not instantaneous, and in the interim the alternator continues trying to charge pu the system to ~13.5V.
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Thanks! I get it. The point of the secondary kill circuit is to reduce the amount of time it takes to get the alternator fully off-line.

Now, just out of curiosity, what harm is caused during this duration of time if the alternator main circuit is still connected to the battery, as my original question asked?