donk,
"I doubt very few operational staff would know what 1 looks like"
So, according to the above, if a 777-300 lost an engine, most "operational staff" (i.e. valid ATCO's/ATSA's) wouldn't have a clue how many serviceable engines the crew had left.
Air Traffic Control is a profession. The "operational staff" are professionals.
I take it from this that you have a 'management' or HR/HF background.