The manufacturer might access it, Apple states they don't, Google and Samsung I'm not sure. A bad actor with 0days might too.
Screens are for playing what I send to them. Not for running their own apps or network traffic.
I would pay more for dumb screen TVs.
It does seem harder to tape the phone camera since the in/out motion into your pocket I imagine would remove the tape.
For the front camera that's a lot more difficult. You could probably modify one of those flexible screen protectors to black out the camera, but it'd be very inconvenient to take off.
Maybe there is some niche android phone that offers physical shutters, similar to the ones on Lenovo laptop webcams
Put aside everything unethical and unworkable about it. Probably cheaper to lobby for a think-about-kids camera ban for products weighing less than 250g or contains transparent window apparatus that may or may not be curved in diameters larger than 10mm for fire risks or something.
That's a bad idea on so many levels.