Steel on road obeys the coefficient of friction… until it starts cutting into the road. Unless you're very light, that's going to happen if you're going an appreciable speed wearing figure skates and then try to stop.
Yes; anything cuts into anything else if you concentrate enough weight into enough of a small area, or there are other extreme factors involved like things melting.
E.g. A carbide bit milling a stainless steel object is clearly not following carbide-on-stainless coefficient of friction.
(I promise I will keep that in mind the next time I attach skates to a bicycle frame.)