> you can’t help but wondering it’s indeed not the interest of USA to have once unconquerable empires like Persia to be thriving and realize their full potential.

This is rather conspiratorial.

Great Britian and Russia have been involved in Iran since the 19th century (example[1]). They both invaded during WW2[2]. Britian left after the war but Russia stuck around. As the cold war began, the USA also got sucked into the mess in the middle east because Russia already had a presence there[3]. The US involvement is often portrayed as the beginning of this mess (just like you did), but it really isn't.

I promise that at no point did anyone involved say to themselves "I sure am scared of a modern Persian Empire". The country was simply caught up in the geopolitical chess game between world super powers. That doesn't make it right, but that's what it is.

[1] https://en.wikipedia.org/wiki/Reuter_concession

[2] https://en.wikipedia.org/wiki/Anglo-Soviet_invasion_of_Iran

[3] https://en.wikipedia.org/wiki/Iran_crisis_of_1946