There's only so many ways a "flip" can open.
Why flip up?
- Right = hits and blocks your thumb if you're righthanded
- Left = hits and blocks your thumb is you're lefthanded.
The only logical direction for a mass-produced device is upwards or downwards. Both variants exist for phones (down, up)
Since the Star Trek communicator flip cover is metallic, I wonder if it's used as an auxiliary antenna. That could be a reason why it specifically flips up and not down.
When closed, the flip acts as a cover. In Star Trek, it prevents you from pressing buttons (the classic butt dial, or simply prevent you damaging the buttons, or the buttons hurting you when the device is in your pocket).
On flip phones, it protects the screen and minimizes the phone's size, making it easier and safer to carry in a pocket (more spherical, as opposed to a long object).
Why a flip hinge?
- If you don't attach the flip to the device, it may get lost. You also need to put it somewhere whenever you open the device.
- If you loosely attach the flip, it's going to flop around when you're moving around. This may damage the flip/device/surroundings.
The only logical decision here is to use a hinge. It's sturdy, ensures you never lose the flip, and prevents it from flopping around. It also helps one-handed use of the device, compared to a cover that clips on and needs to be taken off.
Additionally, in the phone's case, the hinge is big enough to allow for the video cable to go through the hinge from the device to the screen.
Note that phones experimented more: flipping, sliding, unfolding, ... Comparatively, the Star Trek communicator lacks variation.