During WW2 a great deal of research and development work went into the use of mild (softer) steel cartridge cases, primarily due to critical demand for copper and brass (copper-zinc alloy). Millions of rounds were produced in .30-06, .45ACP, and other calibers.
The Soviet-bloc nations, as well as China, manufactured many millions of rounds of small arms ammo using mild steel cases.
A number of innovations were involved. Steel cases were typically coated with lacquer to minimize corrosion, and specific lacquers were developed to facilitate functioning in automatic and semi-auto weapons. Internal case dimensions of steel-cased cartridges differed from those of brass-cased ammunition, so powder charges needed to be adjusted accordingly. Some calibers (.45ACP was one) required extra attention to keep bullets from being forced back into the cases during the feeding cycle, and one method was the use of asphalt-based cement to secure the bullet into the case mouth.
Some stories persist indicating that the steel cases caused damage to extractors, ejectors, etc. Those may be anecdotal, or they may indicate real problems; whichever, the decision makers seem to have chosen to meet the need for sufficient ammunition to the troops, with wear and tear to the weapons being a secondary consideration.
The most common alloy used for small arms ammo is a 70/30 alloy of copper and zinc, which is a pretty strong metal that still allows for sufficient expansion and contraction during the discharge cycle to properly seal the breach. I was not involved in the development of steel-cased ammunition, but I suspect that this was a primary concern in the specific steel alloys used for the purpose.
Regardless of what some may think (or worry about), the soft steel alloys used for cartridge cases are necessarily much softer than anything used for barrels, chambers, or other critical firearms parts, so I would not waste much time worrying about undue wear and tear from using such cartridge cases in my guns.
Steel-jacketed bullets are another subject entirely. Armor piercing bullets (tungsten carbide core in steel jacket) is another subject entirely.