Putting a screen protector on such a large screen is a pita.
The little debris parts that will come in between will get a nice sort of halo under the protector, coz otherwise you could hardly notice them, which would be a shame.
My 4.7" phone has one "foggy spot" outside the display, fortunately. The smaller dslr display also, and so it was with several older phones.
I would polish scratches only, if they eh, scratch tissue, both cloth and body, you would not want to bleed or buy new clothes constantly.
So far I needed that only for plastic case scratches. A cheap lighter used to open a bottle of beer can ruin your trouser pockets, in that case rubbing the thing on some surface makes things better.