If pilots are alive and conscious they will generally be sufficiently aware by other clues, since. Given that ADS-C which MH370 was using is contracted to ATS without a transponder the feedback offrom ATS data would cease.
There are only so many alarms you can bombard a pilot with before it becomes a counter-productive distraction in an emergency.
It is just a presumption that MH370's transponder was turned off since the Flight Aware website notes that MH370's transponder did briefly send signals again about three hours after take-off at 03:48-03:51 MYT.
Because these transponder returns were prompted by MH370 flying through civil radar coverage and being painted by civilian PSR radar then it may be that it flew through a gap in radar coverage and MH370's transponder was not switched off at all.