In that circumstance they're trying out untested engines for the first time, and no doubt no oen wants them doing in near Earth. Note that they go straight to warp from Earth orbit at the end of the movie, which refutes the idea that it's dangerous.
I think that's speculation. We don't know how long it is from Kirk's final words to the warp-out.
And I don't see how trying out the engines requires you to get to Neptune or anything.
Sorry, didn't see Maurice already addressed this.
The notion of getting way outside any gravity wells for doing potentially dangerous FTL stuff is just good manners and safety concerns being addressed.
As opposed to the WTF of calibrating warp engines while on the ground, which is the Orci explanation for the AbramsVerse aberration, you'd do it where the ship lives, in deep space.
If you think that is speculation rather than just reasonable extrapolation, I supposed you're welcome to do so.