No teacher (or parent) has ever managed to lock down a computer that was in my possession to a level where I wouldn't get distracted by it. You could shut the power off, and I'd still be poking around the hardware. I spent hundreds of hours programming my calculator instead of paying attention in class. Informative? Yes. Distracting to myself and those around me? You bet.

I completely agree with your phone take. There is no level of administrative control that can remove the distraction from the device.

Why would you think laptops are different?

We could reduce it to the level of distraction of a notebook and pen. Grayscale would help.