Why wouldn't it allow encryption? Can't anything that sends and receives packets be able to be encrypted?

The restriction is because commercial activities are prohibited over amateur radio, and encrypted traffic would prevent that rule from being enforced.

I believe there's an exception for controlling remote devices when you need to make sure some rando doesn't brick your pricy gear.

Not if the law forbids encrypted connections over Ham frequencies :)

Oh I see. A policy restriction and not technical.

Is that a privacy issue or some other factor?