Central Airlines (Fairway, KS):
Why are Central Airlines flights posted by tail number and not flight number? Note N716TC as an example.
Because that’s what they file and fly under.
Is this some sort of trick question? 
LOL!! No, not a trick question, but I guess it sounded like a stupid one. I should rephrase it.
Version 2:
When all other airlines (even the little bank-check carriers flying Cessnas) file their flights by a flight number, why would Central Airlines not use their own flight numbers and file their plans by tail number instead?
The question is not why FA posts by their tail number (which should be obvious) but why Central Airlines prefers tail number over flight number in contrast to the industry standard. What makes them use a different standard?
Is that better now?