The flip side of that cultural influence that while Saudi Arabia as a country is relatively young and the land is inhospitable compared with Iran, it also happens to be home to Mecca and Islam's other most holy city, which means the state is disproportionately influential over and vulnerable to adherents of the world's fastest growing and most highly-politicised religion. So it would be quite hard to ignore even if the neighbouring countries had most of the oil and especially if the House of Saud remained ostensibly friendly.

I'm under the impression that the US is mostly following rather than mostly leading in engagement with the Saudi rather than Iran: one country is lead by plutocrats whose relationship with the US is driven by desire to dominate the world oil trade, and the other controlled by powerful revolutionaries and theocrats whose control over an increasingly diverse society depends on invoking the spectre of "Great Satan" as recent history's most dangerous enemy.