mainly this section
You have a point in time where the alternator reaches it's limits.
Before this point, there's no need for a capacitor.
And you have a point in time after that where the battery was called upon due to the dropping voltage level, where the battery actually has risen to the demand, and is fully providing the current that's being demanded.
After this point, there is no need for capacitor.
There's a gap in between those two points in time, where the voltage is initially falling, and where the current flow is rising, where the supply of current isn't meeting the demand for current.
And that gap in time only is milliseconds.
which explains why we really have no use for caps in our cars