Also closing it means Iraq, Kuwait, Qatar and Bahrain have a massive shipping problem, which would really threaten those countries in such a massive way, that it could be seen as an attack on them. Not to mention that oil is shipped to countries all around the world. Basically everybody who is not an oil exporter is going to hate them for doing it.

Also Iran needs to ship oil via the straight as well. Starting some conflict around it, would really hurt their income.