Read between the lines in Amazon's response.

They probably monitor the drivers for lip movements to see if they're talking on the phone, but their monitoring can't differentiate between singing or talking to one's self and talking or singing to someone else, so everyone gets flagged. The drivers know the best way to avoid the ire of management is to simply not move their lips.

It may not be an outright prohibition, but it does have a chilling effect, which makes it as good as one.