Writing Rubric Scoring Idea-Teacher Tip

We use the 6+1 trait writing rubric to score student writing. Each month, the students write about a topic and the paper is scored and placed in the writing portfolio. Usually we attach (staple) the rubric to it and circle the score. I had an idea and my team liked it well enough that we all used them for our writing portfolio pieces. My idea was to just put the rubric for the trait on the writing piece, and then we would not have to staple a rubric to it.

Here is a sample and you can click here to get all example writing pieces (free).

Do you think this is a good idea?
I do not use the handwriting lines paper unless it is a final revised copy. I just want them to write and not worry too much about the writing formation.