The Kurds soundly control a mountain land corridor between Iraq and Iran, and have controlled that since even before the recent attacks. Iran is not in a position anytime soon to close that without air power that they don't have.

I don't think staging light infantry will be a problem but I don't think they'll successfully break out of the mountains, certainly not into any land that isn't already ethnically Kurd (or Baloch, but that's in the other corner of the country).