Again, the initial decision by Iran was to stay in Tuscon, AZ. They negotiated with FIFA a few weeks out from the WC to move their training and stays in Tijuana. This caused everything to change, and could have complicated their visas. As I said, late changes between countries with poor or unstable relationships can really muck up travel plans. That's not shocking, and the decision to switch locations was made by the Iranian team.
They also were allowed to enter 2 days before for the last game. The other two games were held in LA...not exactly a heavy trek. As for support staff, that sucks but visas get denied. Considering the relationship between nations, having people denied visas that are somewhat integrated into the government will certainly raise flags. You seem to want this to be a left vs right political thing, but realistically it's not unusual given the circumstances. The actual unusual part is that the WC happened to be here, which allowed outlier situations to be amplified.