The issue is more that the zinc is applied to prevent rust on the underlying steel case. Zinc itself can corrode and leave harmful (abrasive) byproducts behind when fired. May even flake off and stick to inside of steel chambers. Zinc is an active metal that can, under the right conditions, "self plate" itself to a substrate like steel. Steel cased ammo is notorious for being hard on extractors.

Zinc bullets have are an old concept. They have just gotten attention again because of the high cost of lead and copper. No problems at all if you clean your guns. Galvanic action can cause corrosion otherwise.

Yes, Zinc is normally softer than Copper but there are various grades for different hardness. Used in bullets though, your barrel will be fine with quality cleaning after firing Tom.