There are three levels of mandate that you have to deal with.
The FAA, there might be some special circumstance that I am overlooking, there is no need to file a VFR flight plan EVER.
The school. They might have a requirement that all of their students file a flight plan for all x-country flights. Further, if they hold a 141 certificate, then their requirements almost take on the mandate of an FAA Reg. This is a very valid safety and flight following concern.
Your personal requirements. If you feel that it is required, then it is. As the PIC, you make decisions and personal policies that are almost as important as the rest. If you lose an engine, and go down in a field, where should the rescuers look?