To the OP:
Let’s replace “שלוחו של אדם כמותו” with another Halacha to crystalize the question.
Why can’t we just take it for granted that the time to light candles on Erev Shabbos is 5:08 without the “mechanics” behind it?
Obviously, you need to understand why the time to light on a particular Friday is 5:08 in order to apply that knowledge to a different week.
The same idea is true of all other Halachos.