The US Empire barely cares about blowback, they subscribe for a maximalist foreign policy pressure ethos. Like in Domino Theory, they abhor independence lest it coherently spread, and act swiftly and decisively against it like playing whack-a-mole. The ethos doesn't have to deliver perfect results free of blowback, it just needs to be good enough for the interests it serves. Regarsing Iran, this is why it is co stantly threatened and sanctiobed by the US and its cronies. The blowback was too successful so they are still just doing a maximum pressure campaign and constantly threatening war. They take a similar approach against Syria and Yemen. They took a similar approach against Iraq and likely will again.

When speaking of material interest and the US state, using "our" can be ambiguous. I am not of the ruling class of the US, and certainly nowhere near the great financiers and imperialists whose interests are the real ones served by empire. So I would never say this serves "our" interests using this kind of logic. Are you of that class? Often actions are taken against the interests of the non-ruling classes and in favor of the ruling class.

One can make an argument that the citizen US working class is a beneficiary of imperialism, paying far below what they should for imports and having wages propped up by the petrodollar, buy this is challenging to rationalize with the idea that it is simply in their interest to, say, keep Iran subservient to US empire. The public are ignorant to these things and there is no mechanistic connection between their actions and these outcomes except the propaganda appaeatus that manufactures their consent, which is really a top-down monopoly on information that still does not inform them of how this might be in their interest. And even then, it is arguable whether this is more generally in their interest. Undermining the petrodollar might lead to their yolk being removed.

So it is not in our material interests to promote instability

When hasn't the US used the british strategy of balkanization, especially in the middle east? Divide and conquer a cornerstone of their strategy, in the ME, africa, south america, SE asia... literally everywhere.

Mossadegh's government was actively overthrown by the CIA, then the US supported the Shah and his son, and had strong relations with imperial Iran until they were overthrown in the Iranian revolution. The Iranian people refused to accept that right-wing US-puppet and his brutal regime any longer, and there was nothing the US could do about it.