Let me offer some perspective from a pilot.
The reason we don't have HDUs (Helmet Display Units) on both eyes is so we can see everything else without it.
What the HDU is showing is anything from our nose-mounted sensors, either the PNVS (Pilot Night Vision Sensor), which is mounted above the TADS (Target Acquisition Designated Sight), see. They send visual information to computers inside the black boxes inside the two FABs, and those computers translate that as visual information into both the HDU and VDUs in the Pilot's cockpit and Co-Pilot/Gunner's (CPG) cockpit. These are the odd things on the nose of the aircraft. These things contain FLIR sensors that enable use to see excellently at night, gives us normal TV (called Day TV), and allows us to sight our weapons. The TADS contains the Apache's laser, which allows us to paint the target with laser-guided Hellfire Anti-Tank Missiles. The HDU allows us to use these devices so we can target what we want and fire upon them when used in conjunction with the helmet system called IHADSS (Integrated Helmet and Display Sight System). The IHADSS tracks our head movement, and the PNVS/TADS moves and tracks according to what we're looking at. We can also control the 30mm Autocannon Turret this way.
Also in the HDU, we get flight data, and if you look on YouTube for Apache camera sight footage, you'll see a long rectangle on the bottom, and inside that rectangle is a little square. This indicates where the sensor is looking at in relation to the aircraft. If the square is in the middle, it's looking generally straight ahead. If it's to the right or left, it's looking right or left. This can be important especially if you need to show your co-pilot what you are looking at, so he gets a good sense of which way to look, since he can't turn his head toward the back seat in order to see you (the co-pilot gunner sits in the front seat). Next to this will be what vision mode we're in (FLIR,DTV) and what weapon we've got WASed (Weapon Activation Select - We use a lot of acronyms in the Army).
As remarkable as this is, we need to see everything else too. I need to see where I'm going, gotta look at my fuel, altitude, engines, I may have to check my map to see if it jives with the waypoint navigation I have on my GPS (also keyed into the wayfinder graphic on the top of the HDU view). At night, the visual in the HDU is dazzlingly bright, and so often I'll have to swivel it away so I can see with my other eye.
Which ever eye you are dominant with, or prefer to use, the Aviation Life Support Equipment (ALSE) guy can modify your visor to accommodate your preference (he uses a Dremel tool to carve it out of the plastic).