NO ICE CHECKS MADNESS just because the aircraft is not eqipped for flight in icing conditions doesnt mean it wont get it!!!!.
Given the serious nature of airframe impact and induction icing the Pilot should always check for it . He/she is then better equipped to deal with the conditions and able to make the decision on wether to climb or descend.
The ice checks also remind you to use the carb heat, check the oat. I teach my students M A S H T P O I D, it takes about 30 seconds to complete and could save your life. I cant think of a better reason.
I might suggest that if this increases the students workload too much then He or she ought not to be there.
Just my view
