There is more to consider than just the hardness of the metal itself.
The oxides of various metals have significantly different hardness levels themselves, and oxides are formed just during normal use.
Iron oxide (which comes from steel, as it is mainly iron) is significantly harder than copper oxide.
So even when the hardness of the two alloys can be similar, the hardness of the oxides formed during use which are also speeding down the barrel can be significantly different.
Iron oxide is significalty harder than the soft steel it can come from.
In fact the hardness of Iron Oxide is about that of the hardened steel of the firearm barrel.
The oxides of copper are much softer than steel or iron oxide.
Oxides are formed during burning, high friction in the presence of oxygen etc.
There is a lot more at work than just the hardness of the base alloy or metal.
Steel is okay used internaly as a core because it never contacts the barrel, but as the jacket or close to the surface it is very different, no matter how soft of a steel it is.
The communists have invested a lot of money and time into finding the right steel alloys for their bullet jackets and cases.
Most nations that have used steel in the bullets have used it internaly as a core because it is cheaper than lead even though lighter and gives a worse BC.
Some have used it for casings, which is worse than cartridge brass for more reasons than just wear (does not expand and contract as well while retaining its strength), but since it is not in a high speed process with a lot of friction forming oxides, not nearly as bad as a steel bullet jacket.
Launching steel of any hardness and iron oxides down the barrel is a sure way to wear out the rifling of the barrel quickly.
Those nations which have chosen to use it for purposes in contact with the firearm obviously felt the cheaper cost of ammo even with increased barrel wear was a good trade off. In fact it is a good trade off if you don't plan to fire a particular rifle many tens of thousands of times before one side or the other is dead. The lifespan of the barrel, and how long it keeps its rifling with various ammo types is less and less important the less often you plan to shoot it.
So when quickly equiping and arming an army, where growth is more important than maintenance, weapon or barrel life during use is less important than building a lot more equipment and ammunition for the same cost.
The AK platform most of the steel started being used in was already a weapon made to loose tolerances anyways. It is reliable, rugged, cheap to make and replace, and does not need to be that accurate for its intended role. So the steel wearing out and increasing the looseness of those tolerances is not such a big deal.
Some steels will obviously be less damaging than others, but all will be significantly more damaging (increased barrel erosion or "wear") than copper.
