Does a rotary evaporator need a draft chamber and a vacuum pump?
I think you are taking too dogmatic a position overall.

1) Vacuum also increases the rate of evaporation, without boiling.  This is just practical.

2) Your claim that your system is "completely closed" is over confident. What if you are wrong and you have a leak?  Now you are free to dismiss this, but this is the safety issue your adviser is getting at.

In other words, it would be easy to incorporate your practice with industry best practice.