No matter how fine the abrasive is, it's still an abrasive and it will introduce new scratches into the chrome surface at a microscopic level. The chrome layer is usually verrrrrrrrrrrrry thin and too much abrasive polishing will remove that layer. The difference between this and polishing wood furniture is that when you polish wood furniture, it is an additive process where you are adding and leveling a finish of some kind. Using it on chrome works by trading a few large scratches for thousands of smaller ones.
I use WD-40, rags, paper towels and broken popsicle sticks and my fingernails to clean all my chrome. It takes forever but I find it is usually the most-effective/least abrasive method -and is somewhat meditative, too. :)