It’s true that being solely responsible for all these things is tricky. Just from a time management point of view.
Especially if you have to deal with several leaders within the company.
But a certain proficiency in the different areas is definitely important and I also don’t think it is strange that an employer would ask for skills besides sketching and CAD.
In my role, I do assume the responsibility for the ID of a product itself but I also do have to frequently deal with graphic design tasks (make presentations, place artwork on products) or create models.
I don’t have to be an expert in these things but I should have a good understanding.
Personally I think it’s great to be involved in all the different creative fields that make up a product experience. As ID, I am probably the person who knows the vision and story of the product most intimately so being part of the whole process to help carry through a cohesive story is definitely important to me.
I don’t think I would be interested in a job where I was told to only sketch all day and not would be part of the other creative parts.