There's this magical black liquid that comes from the ground and the Middle East has a lot of it.
After World War Two, imperialism became "unfashionable" so instead of out-in-the-open imperialism we've got economic imperialism going on. Which is basically just imperialism, but more dishonest and with more extra steps.
Colonies aren't a thing anymore, so "regional allies" that do regular business with the West are basically the same thing, but it also means Western powers can be had by the balls by people like the Saudis. There's money to be made in selling weapons to the Saudis and they have the largest crude oil reserves in the world. So they're an important regional ally... even though ISIS and Al Qaeda exist because of their funding of Salafist ideologies (like Wahhabism).
Because they're an important regional ally, their national interests become western foreign policy interests. Saudi Arabia and Iran have long standing issues, some of which go back centuries because of the Shia v Sunnis shite, some of which are much more modern points of tension. Specifically, the fact that Iran went from being a UK/US puppet government that was incredibly friendly with the West (even though it was a dictatorship at times) to being very hostile with the West... while Iran has the second largest crude oil reserves in the world, means that the Iranian revolution and rise of the Islamic Republic of Iran was very profitable for the Saudis. Their biggest competitor was essentially no longer competing for Western markets.\
So Saudi Arabia has routinely pushed for the West to go to war with Iran. And for Iran to be balkanized by the various ethnic groups in Iran, meaning those second largest crude oil reserves would no longer be part of one nation. But instead it'd be broken up (and Arabs would have a state in the aftermath of Iran being broken up, which would probably allow for more Saudi puppets in the region and another piece of the oil pie for the Saudis to have more control over the oil.
So that's the long term benefit for Saudi interests, which ties into Western foreign policy interests. As several new countries emerging from the smoldering rubbles of Iran also means new opportunities for new puppet governments (although Iraq and Afghanistan indicate that might not go over so great), which Western governments probably view as more appealing than having one powerful nation in the region that is wholly unfriendly to them.
And in the short term, Saudis would be happy with a war in the Middle East... especially Iran. Plenty of reasons for that: 1.) petrol prices will go up as a result of war - thus a big short term profit for them; 2.) war in Iran essentially guarantees they are victorious in their proxy war with Iran in Yemen - Iran will be busy defending itself from foreign invaders to fight a proxy war with it's old enemy - further solidifying Saudi dominance of the region; 3.) it'll kill a lot of Persians and Shia Muslims - ethnic divides in the Middle East are fucking massive and there's a lot of genuine hate against people for not being the same ethnicity. Let alone for not practicing the same form of Islam.
And there's too much money and power to ever expect economic imperialism to ever go away. If the West backs off, China will be happy to impose it's idea of global hegemony. If China decides it doesn't want to (which let's be real, they wouldn't make that decision - they'd seize the opportunity with both hands) then Russia or someone else would.
For as long as that magical black liquid that comes from the ground is as important to us as it currently is, we'll always be palling around the US and sniffing around the Middle East trying to influence it in one way or another.