RE: Killed 4 servos at once...
I have left transmitter and receiver switches on until batteries were dead, more time than I can count. NEVER any damage, to any components, except the batteries.
Only thing that MAY have happened, that I can think of, is if the servos were driven over hard against the stops. That could possibly damage the servos, and some receivers, do drive the servos over hard without a Tx signal.