This is the problem with instantaneous communications. If the local security was the responsibility of the local commander instead of some faceless bureaucrat in Washington then the situation might have been much better handled. Instead, the buck got passed until it got to somebody more concerned about getting elected than saving American lives.
It would be much better to give rules of engagement to the local commander (in Italy, it looks like) and let him make the call. BTW, you almost always commit troops with an incomplete picture of what’s happening on the ground. You rely on them to make things go your way once they arrive and if they need help they’ll tell you how much and where.
If you were Admiral Ham, aboard the Stennis I believe, you are removed and replaced, pending investigation. He thought, in opposition to C in C, that assistance of personnel in Benghazi, was warranted.
Looks like his career may be over.
That would be General Carter Ham of Africom who was relieved of his duties 30 seconds after ignoring his order to stand down on the afternoon of 9/11. Good story today in American Thinker showing the chain of command.
It would be a rare occasion, outside of Pakistan, where someone other than the President would be able to order military force used in another country without a state of war.
While your plan sounds good, it is not practical.