Nixon could go to China because he had a huge influx of ex-Democrat white racists in his party ready to let him do whatever the hell he wanted on foreign policy as long as he kept the civil rights movement from getting any further than it already had.  Had China been the major focus of domestic politics at the time, Nixon almost certainly couldn't have gone.  Politics always matters, and when it comes to the issue of opposition to Israel, the vast majority of Iraqis are much closer to Hezbollah's position than the United States'.

Yeah, the US intervened in his selection, but he WAS one of the most democratically elected Iraqi leaders in the history of the country.  And he IS still accountable to an elected Parliament.  All the Dems would do by forcing him to stand with us instead of the Iraqis is inch him closer to assasination or deposition.