I wouldn't use any steel wool on chrome even though some do it. I like the original look of chrome and anything abrasive will leave a spider web effect in the chrome when it is in the sun.
Chromium by nature is a very thin covering over a nickel plating and if you try to polish it out or shine it up, it's very easy to go through the chromium and expost the nickle plating which has a different look than the chrome. The chromium is basically a translucent coating and the shine you are seeing when you look at it is the nickle showing through the chromium.
It doesn't take much to polish through the chromium being it is only a few mils thick.
More reading on the topic...
Chrome Plating - Harley Davidson Community
Chromium by nature is a very thin covering over a nickel plating and if you try to polish it out or shine it up, it's very easy to go through the chromium and expost the nickle plating which has a different look than the chrome. The chromium is basically a translucent coating and the shine you are seeing when you look at it is the nickle showing through the chromium.
It doesn't take much to polish through the chromium being it is only a few mils thick.
More reading on the topic...
Chrome Plating - Harley Davidson Community