In an ILT course; Is there a way the Instructor -PU- only has access to the Assignment feature?

Do you mean the Assignment learning object? Or access for enrolment only?

An instructor identified in the course will have access to evaluate assignments if that's what you’re looking for

https://help.docebo.com/hc/en-us/articles/360020128319-Managing-assignment-as-training-material#01H8PARH36FHJ6HBG4WX7VS01D

Yeah, it looks like setting someone as an instructor is the only way to get them access to evaulate assignments, but unfortunately, that also gives them access to edit training materials. 

I played around and I couldn’t find power user permissions that will let a user only evaluate an assignment. 

What I did find while playing around is if you use a Docebo test training material, and use a file upload question (assuming the assignment is a file upload), then create a special power user profile with the right permissions and set up, the user will be able to evaluate the Docebo test and provide a score to the user.

Here is how I set it up:

Create a PU profile with the following permissions:

• Course View
• Course Evaluate

Then assign the following resources to the user:

• Course - select the ILT(s) they would evaluate
• User/Group/Branch for the people who would be enrolled into ILT

Next, enroll the user into the session (as a site admin, you would be able to enroll the user into the session after the session has taken place)

This will give user the ability to access the course reports and they review the Docebo Test training material and download what ever file was uploaded to the Docebo test.  Then the user should be able to give a score to the Docebo Test.

It is a tedious work around, but it would give the user the visibility they would need to evaluate something in the ILT course without being able to access the training materials or edit enrollments.