Scoutbook recommends leaving them with Full Control only if they are technology savvy and know what they are doing.
Full control does not mean they are a Unit Admin or even a Den Admin. These are separate roles that only the unit subscription owner can grant to other adults.
Full control does not give the parent rights to your den/patrol or unit either. It is simply a permission between the Scout and the adult that defines how much of the Scout's advancement they can view or modify.
Remember Scouts and parents should be able to check off requirements and leaders have the role of approving them. Parents with Full Control do not have rights to approve the requirements.
So leaving Full Control to parents is not as scary as you think and could offer a better connected experience on Scoutbook.