That capability already exist at the Strait of Hormuz, a far bigger choke point. Although I’m sure Iran would like more control, I’m not sure they are really willing to force that hand. The majority of the other countries in the area have already demonstrated a willingness to work together, with Saudi leading.
Nine years ago, the Hezzies hit INS Hanit with a Chinese C-802 missile. The Iranians provided the tech support. So there’s some history of using proxies there.