That's basically how this works, but manufacturing electronics at a massive scale requires some more flexibility. For example, capacitors have a pretty large tolerance (sometimes +/- 20%) and LEDs have quite a bit of variety in what voltages they'll work at. So for some people the LEDs might last 3 seconds, for some they might last 5s. Using a capacitor also means the LEDs will fade slowly instead of just turning off sharply.

If the LEDs come from a different supplier one day, who is going to make sure they're still within the spec for staying on for 3 seconds?

(And yes, I have long since parted ways with Apple)

Edit:

And to add on: That capacitor needs time to charge so now the LED doesn't actually come on when the sensor comes on, it's slightly delayed!

Thank you for the clarifications. Armchair (well, workbench) engineering strikes again haha!