Well yes, but there's a basis for why such anti-Western ideas exist, which is that the West can choose their own leaders, while we cannot truly do so...
So IYO it would have been better to let the Soviets pull off their version of the 1953 coup, let Iran be somewhat pro-Soviet for ~25 years while losing legitimacy, then wait for a revolution where the revolutionaries chant "Death to the Soviet Union"?
Legitimacy can be won, albeit slowly, as pretty much every foreign-supported revolution showed. The Shah had plenty of time to win his, but he failed.