Not overkill, but a terrible idea in general. Players outside of your field of view can still affect you, for instance you need to be able to collide with a player standing behind you if you step backwards, and even ignoring direct interaction with players outside your FoV, you don't want to have to wait the round trip time to get updates about other people every time your view changes slightly.
Yes, a simple binary toggle (do not send anything behind player's back) will result in substandard experience, but what you can do, in addition to just distance-metric based interest management, is to further throttle down the update rate of objects behind the back. You're right about the RTT; the server would need to use a larger frustum (based on an estimation of how fast the client might be turning the camera + with RTT factored in) than what the client uses to render. Finally, what you can get away with also depends on the camera type: is it first person? Third person? Diablo-like?