It's very common to have an FCY to gather some control over the field and then BFA to bring them into the pits. Once there, if it is decided by the appropriate authority that they must move up to S/F for some reason, then it is simple.
I'm not sure why they need to be on the front straight as opposed to the pits, but it was simply a by-product of the overall situation as things progressed.
And you are correct, Steve. The Steward should indeed be making those Red and Black Flag calls. At least as soon as he/she is properly informed, and has a chance to catch up to the reality of the situation. What is a good time frame for that to efficiently occur? I suppose that it depends on the severity of the situation, and how much radio traffic there is to cut through at the time.
Otherwise, and historically, the communicator(s) in Base Comm are forced into the position of making hard and fast decisions based on the information available from observers on and off of the course, then make every attempt to act in accordance to those regulations to the best knowledge of those individuals in Base Comm, as they may have read, studied, discussed and understood those regulations.
Here I go throwin' the 'book' at it again, but with numerous Asst. Stewards, and Asst. Race Chairpeople for various elements of the race weekend, the processes of operations weakest link is really the most important, and dangerous element of the event; true control of the cars of course. The Steward, and in some cases the Race Chairman are the authorities that carry the responsibility of those calls and safety controls. Command flag calls usually need to be more immediate than are allowed under the current operational deployment of those responsible individuals.
Argue as one might, but "Control" is NOT the communicator(s) sitting up in a tower with a headset, a microphone and a logged record. "CONTROL" is the combination of efforts of those individuals assigned the responsiblity of knowing, applying and enforcing the sanctions regulations for the events' control. From communication from the turns, the Safety/E-Crew teams, Pre-Grid... and so on. Every specialty is an element of control. The Steward, the Race Chairman, the License Director. These are the people that are ultimately responsible for the efficient operation and "CONTROL" of the race event and all that it entails.
I expect some, "That's the way we've always done it." retort, but it's time to look at some of these operational priorities as Conference continues to grow and become less amateur and more professional to accomodate a demanding market to do so.
But I am merely an informed observer. FWIW.