Steel wool, be it plain or in the form of S&S pads, will in fact leave micro-scratches in chrome plated surfaces. Depending on the quality of the plating, it may become obvious quickly or it may take years, but eventually it will affect the appearance of the part. For those who don't believe me, all I can say is get a decent magnifier and look a bit closer at those chrome plated parts you've been scrubbing with steel wool on a regular basis.
Abrasives are for those who lack the patience to let the solvents work. IMHO, it is best to always start with the mildest approach and only escalate to harsher methods if absolutely necessary. You don't clean your new paint job with compound before trying regular non-abrasive cleaners, right? So why do it with a plated surface?
Jerry