"if the FLT NUMBER is actually used for S mode, why do most pilots simply type the number as, for istance, 3011 and not AF3011 to identify the flight as being operated by Air France ?"'
What you should input is the callsign which appears on the ICAO flightplan as that is what the ATC system is looking for. If pilots are abbreviating their callsign, they are doing it incorrectly.