Is this a student project that you need to turn in?
Or is it a small project that will go in production?
If it is the former then is assume your professor has defined that there needs to be a copper zone and that is why you add one. (Without thinking as to why it would make sense.)
Having a copper zone on the back side is normally done for a reason. In most cases because you want better ground connections for EMC/EMI reasons. (With better i mean low impedance)
In your case it looks like there are no connections missing that the copper zone could possibly take care of.
KiCad only fills zones (that have a net assigned) if they are connected to a pad in one way or another. This can happen by using a trace, a via or the zone is in direct contact with the pad.
More details can be found here: Filled Copper Zones not showing up in Gerbers/Printouts/3D view - #9 by bobc