Shiny cookie sheets? What are those. I have had mine for it seems like eons. The edges get a quick swipe with Brillo. The rest of the sheet I get any food that may have stuck on. That is very seldom. Over the years they seemed to have become non-stick on their own. And I leave them alone with just a quick wash with hot soapy water and a good rinse. Like Kate, they have develop a patina and I wouldn't mess with that for any reason. Now the underside. Don't look. I think that is just part of their charm. And I don't cook any food on the underside. So I don't care.
If I am going to use the sheets for any cooking as to baking, I cover the pan with heavy duty foil. No mess to clean up.
I refuse to spend the last years of my life cleaning and scrubbing needlessly.