Spot on.
You don't have to, but to give everyone an easy day, it is best to. The last thing a busy controller wants to sequence at the last minute is you while you are submitting all of the info on a FPL over the radio. This is asking for a loss of control accident too from your end - unless you have a gucci autopilot.
The flight plan cuts out handover phone calls to the next sector by the controller. They all get a printed strip (you hope - not always) and all they do is press a button, say that G-XXXX is FL 80 tracking to XXX for a Zone transit of XXX. They then hand you to the next freq. Job done.