A and C
Could it be that the airliner procedures are based on the much higher airflow speeds and having to allow for consequent errors in the OAT measurement? I'd imagine the penalty for frozen up pitot(s) would be nasty when in auto throttle mode?
There cannot be anything wrong with having the pitot on all the time, except the CFI will moan because he doesn't want to pay for burnt out pitot heaters (most trainers I flew in had the heater burnt out years ago)