You mean it would have led to the theft of an enormous amount of western owned infrastructure which in and of itself would have been grounds for war?

But no, this comment is pretty revisionist. The Shah was already the monarch there. Mosaddegh was not "left leaning." The 1979 Revolution was. Mosaddegh's nationalization was just a naked attempt to acquire wealth for his state and not anything ideological. Meanwhile the 1979 Revolution was overtly supported by communists. And on top of this, you're omitting Mosaddegh's autocratic attempt to seize power himself against the parliament prior to the US backed coup even happening.

To sum it up, the mistake I'm correcting is you are taking a chain of events where "A happened prior to B which happened prior to C" and are trying to draw casual links from "A caused B which necessitated C." It's a textbook fallacy. In fact, you're completely glossing over the very glaring "in spite of" relationship between B and C in this case as Western powers successfully staved off an Islamic takeover of the country for a few decades until the West dropped support due to a wide variety of reasons.