Not just iron man. A lot of leading characters that have to receive injuries as part of the plot often injure their non dominant hand/arm/leg so it seems serious but not debilitating. Most people are right handed so it’s the left side that gets injured.
Also, you can’t say the left arm keeps getting injured in MCU films when that collection showed him getting his arm injured in Civil War, and then showing the lasting effects of the injury afterwards. That’s writers being consistent, not repetitive.