Yes I know steel wool is not soft.

The difference is that abrasives in sponges and things like that are usually aluminum oxide or carborundum which are VERY hard materials with vary sharp points on the particles. These sharp corners will scratch and damage the chrome or hard nickel plating on the probes. They can even start removing the plating.
Steel wool is long thin strands of steel. It is not high grade hard steel but low grade mostly iron steel. The steel should be much softer than most plating on leads, that is if they are of any kind of quality. The strands of steel will have more of a wiping acting rather than a digging scratching action on the plating. Even if the coating is softer, the strands will do much less damage than sharp almost as hard a diamonds little rocks digging into the plating.
Yes the preference would be to use no abrasive type of material in any form. The materials used in the probe grips are not usually very agreeable with with many solvents. When the probes are molded, either the mold is sprayed with mold release which then gets on the probe tips, and/or the plastic from the probe grips gets on the probe tips. This is the cause of the bad contact and what needs to be cleaned off. So to clean the probes only with solvents and not with any type of mechanical cleaning would also start degrading the probe grips.
What would be the best chemicals to clean the probe tips? Probably toluene, acetone, and chlorinated solvents like Chlorothene NU or VG but they would also be very hazardous to use for the probe grips and the person doing the cleaning. I other words, anything that is actually going to dissolve the plastic coating on the probe tips from the molding process is also going to dissolve the grips and is going to be hazardous to the user.
If the probe tips have lousy plating and have an oxide layer then chemicals like the above will do nothing and only an abrasive is going to help or some kind of electrolysis. Using the mildest form of abrasive possible, steel wool in this case, is the preferable tool.
I also meant to say that gold plated tips should never be cleaned with any abrasive. That plating will get destroyed immediately. Use the least mechanically aggressive method possible and use isopropanol or something similar.