I think we should be careful using wording like that. The Iranians have agency and can do things on their own. Just because the west meddled in things doesn't give us the right to claim the results as ours, be they good or bad.
We've done it a number of times in South America as well. I'd say there's enough data points to believe that we punted them into the downwards spiral that they're struggling in now.
The royalist regime installed by the CIA in ‘53 replaced a popularly elected social democratic government. I won’t say the shah was ever popular, but there was not massive opposition at first. In part due to repression, and in part due to increased liberalization (e.g. rights for women), industrialization, and increased wealth (which I believe would have happened with the prior regime as well).
But those other factors don’t increase linearly or automatically and soon repression was the only way the Shah’s regime stayed in power.
To many people the Revolution seemed at first like a breath of fresh air. After all it overthrew the hated regime. This is the classic difficulty for all movements (from free software to regicide): different paths intersect and then diverge. Khomeini was indeed quite popular (though far from universally) but his followers were the largest (practically only iirc) organized opposition and so, like the Bolsheviks/Mensheviks (despite the name, the Bolsheviks were in the minority), they pushed the guys at the top of the hill off, and maintained their own balance up there.
Compare that to the French Revolution where there was no faction large enough to do this: they pushed out the Ancien Régime but then muddled around aimlessly and violently until someone was able to secure the high ground.
So Khomeini was “popular” in the sense that lots of people were favorable to his movement in the moment, but not “popular” in that the movement had a widespread base of support. Like the prior regime, after a short honeymoon they could not rule without repression.
Unfortunately there is no external opposition that could come in and restore democracy. So a complete overthrow of the current regime is quite unlikely.
Of course Iranians have agency as individuals; but it's very clear at this point in history that most of the 20th century has been dominated by US strategic decisions, and that "the US and UK supported a coup" is factually true.
I am Italian, I believe Italians have agency, too, and yet some of our past governments were inches away from being "guided" in a different direction by the CIA or other US agencies [0].
[0]: https://www.wilsoncenter.org/blog-post/all-feasible-means
Which country?
From the mid- to late 19th century, Guatemala suffered chronic instability and civil strife. Beginning in the early 20th century, it was ruled by a series of dictators backed by the United Fruit Company and the United States government. In 1944, the authoritarian leader Jorge Ubico was overthrown by a pro-democratic military coup, initiating a decade-long revolution that led to sweeping social and economic reforms. A U.S.-backed military coup in 1954 ended the revolution and installed a dictatorship.[10]
From 1960 to 1996, Guatemala endured a bloody civil war fought between the US-backed government and leftist rebels, including genocidal massacres of the Maya population perpetrated by the military.
A revolution is not about agency. You make a mockery of the whole idea. Agency implies what the majority wants. That is what they had with democracy which the US ruined. They took away Iranian agency. The revolution later happening is not a good example of agency. A revolution rarely express the popular will. Instead it gives power to those people most capable of using violence.
Democratically inclined and freedom loving humanitarians will frequently lose in a civil war as they lack the violent behavior to win.