Nope, it’s been rubbed down to the base metal.

1. It’s old and worn down
   2 it’s not old, but inferior
   3 you’ve obsessively cleaned it, &/or
   4 your cleansers and scrubbers are far too abrasive

I feel you need to replace the faucet. It’s a quick fix. I only use Moen and Kohler faucets. I recently redid all my bathrooms and used Moen faucets. I clean the faucets with Windex and a paper towel. They always look great.

Many faucet/hardware brands offer a lifetime warranty on the finish. When you get a new faucet and something like this happens again, they would exchange it at no cost. I've had finish issues with door hardware (Kwikset) and a faucet (Price Pfister) in the past and got quick and easy replacements from the manufacturer. However, I did have the original receipt/was the original owner of the house.