So who signs off on a specific attack on Iran? Do some risk management. Have a decimal point in the wrong place and you have another Chernobyl. I have a hard believing that is below anyone's paygrade. Fix the economy, fix healthcare, fix immigration, fix Muslims, fix America, fix the stock market, if that is all you have to say before you go to lunch, anyone could be President, as well as keep their old job.
The President as Commander In Chief gives the US military its orders, which all members of the military are obligated to carry out as ordered. The President out-ranks all other military officers and makes the decisions on the highest level. Or as George W. Bush once said, he is the decider.