Way to set a field value once, but not to edit it

I was hoping that with field_permissions there would be the possibility that a user of a role could set a field value once but not be allowed to edit it.

Setting the value initially is of course possible, but unfortunately only in the node-add form, not in the node-edit form. There the user is only allowed to set the value if he has the field permission "Edit own value for ..." or " Edit anyone's value for ...", which he should not have in my usecase.

A module "Readonly field widget per role" would help here, but I didn't find any. Wouldn't it be best if field_permissions could do that?

Originally I had assumed that the field permission "Create own value for field ..." refers to whether a field value already exists in this node and not to whether a user is in add or edit form.