The privacy indicator on iPhones is just a green dot on the display. I don't think that's really possible to link to the same power supply. It'd have to be a separate light like on MacBooks.
(Thankfully MacBooks do at least physically disconnect the microphones if you close the lid.)
It could be independent of the OS software if it were a design goal (e.g. in safety-critical applications you sometimes have display controllers that have dedicated hardware layers for important indicators that are driven independently of the main display feed, something Apple could easily replicate given their level of integration)
And of course it doesn't have to be on the display, given they already have a cutout island in the display where they could place such a thing.
(Thankfully MacBooks do at least physically disconnect the microphones if you close the lid.)