I got into the topic over on the AR side Here. I know I saw one test where it took 10,000 rounds of steel cased to ruin a Bushmaster 5.56 barrel, but what about AKs and SKSs? I've never heard of one getting shot out.

Jim Fuller retired a Krink he built recently.  As I recall it was rebarreled 3 times and he put it up after 100K rounds.  I can't remember the source for the info though.

Go over to the AK Abuse discussion in the AK Discussions section. Henderson defense wears out a lot of guns.

I have never personally shot out an AK barrel but I have access to AK47s that have had their barrels shot out.  I do not know the round count.  I have never seen an AK74 with its barrel shot out, but with the higher velocity and somewhat long bearing surface, I suspect they would wear out a barrel faster than a 7.62x39 AK.  Which is not to say that either wears out quickly.

That 10,000 round test people like to quote for 5.56 is informative, but not definitive. Heat kills, and that firing schedule was brutal.  I'm not convinced there would be a major difference in barrel life between ammo types under a more normal firing schedule.

I have some government reports that state stellite-liners do not stand up well to double-base propellants, like ball-powders.  I have no idea what kind of powders the russians use, or the effects they have on chrome plating.  I assume they would be a lot harder on the chrome as well, but I don't recall seeing that mentioned anywhere.

I have a Hungarian AK with many thousands of rounds through it. Lots of steel core surplus from back when it was cheap. You can see places in the rifling where the chrome plating has chipped or peeled away.

Far from "shot out" but visible wear nonetheless..

The subject should be better defined; 'Steel case' means the cartridge case is steel. 'Steel core' means the bullet has a steel insert. In neither of these cases does steel come into contact with the bore. The only case it does is with bullets that have a 'bi-metal' jacket which is soft steel coated in copper. This type of bullet has been shown to be no more abrasive in a barrel than a copper jacket.
Even steel core bullets with a bi-metal jacket have lead around the core which allows the bullet to be deformed by the rifling, which is the reason they are no harder on a barrel than any other bullet.
The AK was made for this ammunition so assuming regular cleaning/maintenance, there should be no reason why you would expect the barrel to wear out faster than expected using it. What wrecks barrels is rapid fire, heat and extreme round count in short time periods. Not much of a problem now, but many AK barrels were wrecked by shooting corrosive ammo and not cleaning properly afterward.