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!